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Railway. 


543  Pages;   1 00  Illustrations;  6  Folding  Plates;  65  Tables; 
8vo.  Cloth.   Price  S5.00. 


MASONRY  CONSTRUCTION, 

BY  IRA  C.   BAKER,  C.  E. 

PROFESSOR  OF  CIVIL  ENGINEERING,  UNIVERSITY  OF  ILLINOIS. 


PART  I.    MATERIALS. 

Chapter         I.    The  Natural  Stone. 
II.     Brick. 
III.     Lime  and  Cement. 

PART  II.     PREPARING  AND  USING  THE  MATERIALS. 

Chapter      IV.  Mortar,  Cement  and  Artificial  Stone. 

V.  Quarrying. 

VI.  Stone  Cutting. 

VII.  Stone  Masonry. 

VIII.  Brick  Masonry. 

PART  III.    FOUNDATIONS. 

Chapter      IX.  Introductory. 

X.  Ordinary  Foundations. 

XL  Pile  Foundations. 

XII.  Foundations  under  Water. 

PART  IV.    MASONRY  STRUCTURES. 

Chapter  XIII.  Masonry  Dams. 

XIV.  Retaining  Walls. 

XV.  Bridge  Piers. 

XVI.  Culverts. 

XVII.  Masonry  Arches 

APPENDIX.      SPECIFICATIONS  FOR  MASONRY. 

General  Railroad  Masonry'. 
Masonry  for  Railroad  Buildings. 
Architectural  Masonry. 
Laying  Masonry  in  Freezing  Weather. 

A  full  Index  to  the  above  will  be  sent  free  cm  application. 

This  is  the  only  book  on  the  subject  of  Masonry  Con- 
struction; it  is  very  complete,  very  practical,  and  it  has  at 
once  taken  its  place  in  Engineering  literature  as  a 
standard  work. 

Sent  post  paid  on  receipt  of  price,  by  the 

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ENGINEER'S 


FIELD      BOOK 


BY 


C.  S.  CROSS,  CIVIL  ENGINEER 


THIRD  EDITION. 


To  which  is  added  much  valuable  information  on  Railroad  Surveying  and 

Construction,  by  the  late  Prof.  Chas.  A.  Smith,  C.  E.,  of  Washington 

University,  St.  Louis,  Mo.,  Wm.  F.  Shunk,  C.  E.  and  others. 


COMPILED  AND  EDITED  BY 

GEO.  H.  FROST,  C.  E. 


NEW    YORK: 
ENGINEERING    NEWS    PUBLISHING   CO., 

1890. 


^    />  1 

i Gx*"T $5-00 

action | 2.00 


Baker's  Masonry  Construction 

Billing's  Water- Works  Construction | 2.00 

Bouscaren's  Specifications  for  Iron  and  Steel  Highway  Bridges 25 

Bouscaren's  Specifications  for  Iron  and  Steel  Railway  Bridges 25 

Buchanan's  Tables  of  Squares 2.00 

Cooper's  Specifications ;  Iron  and  Steel  Highway  Bridges 25 

Cooper's  Specifications ;  Iron  and  Steel  Railroad  Bridges 25 

Cross' Engineer's  Field  Book 50 

DuBois'  Strains  in  Framed   Structures 10.00 

Dunham's  Plat  and  Profile  Book,  20  miles 1.00 

50  miles 2.00 

Fanning's  Water  Supply  Engineering 5.00 

Gilmore's  Limes,  Hydraulic  Cements  and  Mortar 4.00 

Gould's  Specifications  for  Dams  and  Reservoirs 25 

Gould's  Practical  Hydraulic  Formulae 1.00 

Greene's  Bridge  Trusses,  Graphical  Method 2.50 

Greene's  Arches,  "  "       2.50 

Greene's  Roof  Trusses,  "       1.25 

Haupt's  Topographer 4.00 

Henck's  Field  Book  for  Railroad  Engineers 2.50 

Bering's  Bearing  Piles,  2d  Ed 20 

Herschel  and  North's  Road  Making  and  Maintenance 1.50 

Hudson's  Tables  of  Excavation  and  Embankment 1.00 

Jacob's  Storage  Reservoirs  (new  edition) '.     .50 

Johnson's  Theory  and  Practice  of  Surveying 3.50 

Manual  of  American  Water- Works,  1889-90 3.00 

Osborn's  Tables  of  Moments  of  Inertia  and  Squares  of  Radii  of  Gyration,  2d  Ed.    2.00 

Parsons'  Track;  A  Manual  of  Maintenance  of  Way 2.00 

Parsons'  Turnouts 1.00 

•Searles'  Field  Engineering: 3.00 

Shunks'  Field  Engineer 2.50 

'Yrautwine's  Civil  Engineer's  Pocket  Book 5.00 

Wellington's  Economic  Theory  of  the  Location  of  Railways 5.00 

Wellington's  Computation  of  Excavation  and  Embankment 4.00 

No.  1.  Katte's  Specifications  for  Construction  of  Graduation  and  Masonry.  Con- 
tents: Articles  of  Agreement,  Formation,  Graduation;  Masonry,  including 
Specifications  for  Laying  Masonry  in  Freezing  Weather;  Foundations,  Tim- 
ber, Iron- Work,  General  Provisions  applicable  to  all  work.  Indemnity 
Bond,  16  pages.  Price,  25  cents. 

No.  2.  Specifications  for  Standard  Pile  and  Timber  Trestle  Bridging.    Price,  5  cents. 
No.  3.  Specifications  for  Cross  Ties.    Price,  5  cents. 
No.  4.  Specifications  for  Track  Laying.    Price,  10  cents. 

Any  book  in  the  above  list  will  be  sent  post  paid  to  any  address  in  the  United 
States  or  Canada  on  receipt  of  the  price  by  the 

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TRIBUNE  BUILDING,  NEW  YORK. 


CONTENTS. 


PAGE. 
Method  of  Staking  out  and  Keeping  Field    Notes   of   Railroad 

Curves 5-16 

Railroad  Curve  Tables,  for  expeditiously  determining  the  points  at 

which  to  commence  the  Curving 17-30 

Keeping  the  Field  Notes  of  a  Railroad  Survey  from  which  the 

Center  Line  is  Laid,  with  a  Map 31 

Excavation  and  Embankment;  Application  of  the  Prismoidal  For- 
mula   32-37 

Excavation  and  Embankment  Tables 38-43 

Instructions  to  Division  and  Assistant  Engineers  relative  to  Field 

Notes  on  Surveys  for  the  South  Penna.  R.  R.  Co 44 

Engineering  Field  Work.     By  the  late  Prof.  Chas.  A.  Smith,   of 

Washington  University,  St.  Louis,  Mo 45-63 

Regulations  for  the  Engineering  Department  During  Construction, 
prepared  for  the  South  Penna.  R.  R.  Co.,  by  Wm.  F.   Shunk, 

C.  E 65-84 

Howe  Truss  Bridges  (Illustrated) > 85-88 

Table  for  Computing  Right  of  Way  Areas.    Width  100  ft 89 

Pile  Driving  Machine  (Illustrated) .„„.....  90-93 

Metric  Railway  Curves 94^98 


THE    ECONOMIC    THEORY 

OF  THE 

LOCATION  OF  RAILWAYS, 

By  ARTHUR  MELLEN  WELLINGTON. 


Revised  and  Enlarged   Edition,   8vo  cloth,  1,000  pp.,  314  Engravings, 
204  Tables,  $5,00. 


C  O1VTE1VTS: 

CHAP.  1.  The  Inception  of  Railway  Projects  and  Conditions  governing  it. 

2.  The  Modern  Railway  Corporation. 

3.  The   Nature   and   Causes   connected    with   Location   modifying 

Volume  of  Railway  Revenue. 

4.  The  Probable  Volume  of  Traffic  and  Law  of  Growth  therein. 

5.  Operating  Expenses. 

6.  The  Minor  Details  of  Alignment. 

7.  Distance. 

8.  Curvature. 

9.  Rise  and  Fall. 

10.  The  Relative  Importance  of  Gradients. 

11.  The  Locomotive  Engine. 

12.  Rolling  Stock. 

13   Train  Resistance. 

14.  The  Effect  of  Grades  on  Train  Load. 

15.  The  Effect  of  Train  Load  on  Operating  Expenses. 

16.  Assistant  Engines. 

17.  The  Balance  of  Grades  for  Unequal  Traffic. 

18.  Limiting  Curvature  and  Compensation  Therefor. 

19.  The  Limit  of  Maximum  Curvature. 

20.  The  Choice  of  Gradients,  and  Devices  for  Reducing  them. 

21.  Trunk  Lines  and  Branch  Lines. 

22.  Light  Rails  and  Light  Railways. 

23.  The  Economy  of  Construction. 

24.  The  Improvement  of  Old  Lines. 

25.  Grade  Crossings  and  Interlocking. 

26.  Terminals. 

27.  The  Art  of  Reconnaissance. 

28.  Ocular  Illusions. 

29.  When  to  make  Surveys. 

30.  The  Field  Work  of  Surveys. 

31.  Topography ;  its  Uses  and  Abuse. 

32.  Mapping  and  Projecting  Location. 

33.  The  Estimation  of  Quantities. 
Sent  post  paid  on  receipt  of  price  by  the 

ENGINEEKING  NEWS  PUBLISHING  CO., 

TRIBUNE  BUILDING,  New  York. 


RAILROAD   CURVES. 


The  following  tables  show  the  distance  from  the  point  of  inter- 
section of  the  tangent  lines  to  the  beginning  of  a  one  degree  curve, 
the  angle  of  deflection  (=angle  at  centre)  being  known. 

In  the  columns,  under  the  head  of  degrees  and  opposite  the  min- 
utes, are  given  the  distances  in  feet  from  the  intersection  of  tan- 
gents to  the  beginning  of  one  degree  curve. 

To  ascertain  the  distance  for  any  given  degree  of  curve,  divide 
the  distance  given  in  the  tables  for  a  One  degree  curve,  by  the 
degrees  of  the  required  curve,  and  you  have  the  distance  from  the 
point  of  intersection  to  the  beginning  or  end  of  curve. 

EXAMPLE: 

Required  the  distance  from  the  point  of  intersection  of  tangents 
to  the  beginning  of  a  Two  degrees  curve,  the  angle  of  deflection 
being  25°. 

In  the  tables  under  25°,  and  opposite  0',  find  1270.28  which  divided 
by  the  degrees  of  the  curve  (2°)  give  635.14  feet,  the  required  dis- 
tance. 

In  staking  the  centre  line  for  a  railroad  or  a  canal,  stakes  should 
be  driven  down  to  near  the  surface  of  the  ground,  at  the  intersec- 
tion of  the  tangents,  and  at  the  different  stations ;  and  nails  set  in 
indicating  the  centre  point.  These  stakes  serve  also  for  leveling 
purposes  and  are  useful  in  detecting  errors  while  the  work  is  being 
relevelled  and  staked  out, 


6  EAILEOAD    CURVES. 

The  beginning  and  end  of  curves  should  have  reference  stakes 
set  at  right  angle  to  the  centre  line,  similarly  driven  and  marked, 
and  at  such  convenient  distance  from  the  centre  as  will  insure  them 
from  being  displaced  in  making  excavations  and  embankments ; 
and  at  all  the  above  named  points  another  stake  for  numbering, 
&c.,  should  be  firmly  driven  adjacent  to  them. 

The  radius  of  a  One  degree  curve  is  5730  feet.  The  circle  being 
divided  into  360  parts  of  one  degree  (equal  angle  of  deflection)  give 
360  chords  of  one  foot  in  length  at  the  circumference,  and  also  a 
radius  of  57.3  ft.  thus : 

360  114.6 

= =  57.3 


3.1416 

The  chord  of  One  foot  in  length  for  1  degree  =    57.3  ft.  Kadius. 

10    feet  "  "      "       =   573.0 

"  100      "  "  "      "       =5730.0         " 

Or  the  radius  may  be  calculated  by  natural  sines,  thus : 

sin.  1° :  100  ft.  chord  :   :  sin.  89°  30'  :  5730  ft.  radius. 

To  determine  the  degree  of  curvature,  having  the  radius  given, 
divide  the  radius  of  a  One  degree  curve,  5730,  by  the  radius  of  the 
given  curve. 

EXAMPLE : 

Required  the  degree  of  a  curve  having  a  radius  o£  1000  feet : 
=  5.73°  =  5°  43' 48" 


To  determine  the  length  of  the  curve  having  the  angle  of  deflec- 
tion given  ;  divide  the  angle  of  deflection  (=angle  at  centre)  by  the 
degrees  of  the  curve,  and  you  have  the  required  length  of  the  curve. 
If  there  are  degrees  and  minutes  in  the  angle  of  deflection,  the  min- 
utes should  be  converted  into  decimals. 

EXAMPLE : 

The  angle  of  deflection  being  20°  49',  |J  =0.816.  Then  20.816  is  the 
distance  for  a  One  degree  curve ;  if  for  a  2  degrees  curve,  divide  this 
result  by  2 ;  for  a  3  degrees  curve,  divide  by  three,  and  so  on. 

The  angle  of  deflection  being  given,  the  following  results  are 
readily  determined : 


RAILROAD    CURVES. 


Angle 
of 
deflection 

Degree 
of 
curve 

Deflection 
per 
100  feet. 

Radius 
of 
curve 

Dist.  from 
intersec.  to 
beginning 
of  curve. 

Length 
of 
curve. 

20°  49' 

1° 

0°30' 

5730. 

1052.49 

2081.6 

20°  49' 

2° 

1°00' 

2865. 

526.24 

1040.8 

20°  49' 

3° 

1°30' 

1910. 

350.83 

693.8 

20°  49' 

4° 

2°  00' 

1432.5 

263.12 

520.4 

20°  49' 

5° 

2°  30' 

1146. 

210.50 

416.3 

To  ascertain  the  radius  of  a  curve,  having  the  angle  of  deflection, 
and  the  distance  from  intersection  to  beginning  of  curve  given. 
Find  the  distance  for  the  angle  of  deflection  in  the  tables,  which 
divided  by  5730.  gives  the  natural  tangent  of  half  the  angle. 

Then  divide  the  distance  from  intersection  to  beginning  of  curve 
by  the  natural  tangent  of  half  the  angle,  and  you  have  the  radius. 


EXAMPLE : 

Required  the  Radius  of  a  curve,  the  angle  of  deflection  being  20°, 
and  the  distance  from  intersection  of  tangents  to  beginning  of 
curve  225  feet. 

Under  20°  and  opposite  0'  in  the  tables,  find  1010.37,  which  divided 
by  5730  feet  gives  the  natural  tangent  0.17633.  Then  225  ft.  divided 
by  0.17633  gives  the  radius  1276  feet. 


FIELD  NOTES  FOB  A  ONE  DEGREE  CURVE. 

Bearing  of  1st  tangent N.  20°  W. 

2d.         "        N.  40°  W. 

Angle  of  deflection  by  needle    ......    20° 

"  graduated  card    ...    20° 

The  angles  measured  with  the  card  are  the  most  reliable ;  but 
the  angles  by  the  needle  although  it  often  indicates  a  slight  differ- 


8 


RAILKOAD    CURVES. 


ence,  serves  as  a  check  to  greater  errors  which  may  arise  in  reading 
the  degrees  on  the  graduated  limb  of  the  instrument. 
*  Station  No.  506.2000    Intersection  of  tangents. 

—  10.1037    from  intersection  to  beginning  of  curve. 


*  Station  No.  496.0963    point  at  which  curve  commences. 
4-   20.0000    length  of  curve. 


Station  No.  516.0963    point  at  which  curve  terminates. 


DEFLECTION   FROM   TANGENTS. 


Stations. 

Length  of 
chords 
in  feet. 

Deflection 
from 
tangent. 

REMAKES. 

496.096 

1C         « 

«      a 

*  Beginning  of  curve.  . 

497. 

90.37 

0°    27 

1°  to  left.  (Tang,  due  N.) 

498. 

100.00 

0°    57 

499. 

100.00 

1°    27 

500. 

100.00 

1°    57 

501. 

100.00 

2°    27 

502. 
503. 

100.00 

loo.oo 

2°   57 
3°   27 

*  Change  point. 

504. 

100.00 

3°   57 

505. 

100.00 

4°   27 

506. 

100.00 

4°    57 

507. 

100.00 

5°    27 

508. 

100.00 

5°    57 

509. 
510. 

100.00 
100.00 

6°    27 
6°   57 

*  Change  point. 

511. 

100.00 

7°    27 

512. 

100.00 

7°    57 

513. 

100.00 

8°    27 

514. 

100.00 

8°   57 

* 

515. 

100.00 

9°   27 

516. 

100.00 

9°   57 

516.0963 

9.63 

10°   00 

*  End  of  curve. 

(Tangent  N.  20°  W.) 

RAILROAD    CURVES. 

FIELD  NOTES  FOR  A  TWO  DEGEEES  CURVE. 

Bearing  of  1st  tangent  N    10°  W. 

2d  '•    N    30°  W. 

Angle  of  deflection  by  needle 20° 

'•  "       by  graduated  card 20° 

Station 506.200  intersection  of  tangents. 

5.052  from  do.  to  beginning  of  curve. 

Station. . . .  501.148  point  at  which  the  curve  commences, 
-f-  10.000  length  of  the  curve. 

Station 511.148  point  at  which  the  curve  terminates. 


DEFLECTION  FROM  TANGENTS. 


Stations. 

Length  of 
chords  in 
feet. 

Deflection 
from  tangent. 

REMARKS. 

501.148 

»»         •> 

0°     00' 

*  Beginning  of  curve  2°  to  left. 

502. 

85.20 

0°    51 

(Tangent  N  10°  W.) 

503. 

100.00 

1°     51 

504. 

100.00 

2°    51 

505. 

100.00 

3°    51 

506. 

100.00 

4°    51 

507. 

100.00 

5°    51 

*  Change  point. 

508. 

100.00 

6°    51 

509. 

100.00 

7°    51 

510. 

100.00 

8°    51 

511. 

100.00 

9°    51 

511.148 

14.80 

10°    00 

*  End  of  curve. 

(Tangent  N  30°  W.) 


10  EAILEOAD    CUBVES, 

In  curves  of  great  length,  the  instrument  should  be  moved  for- 
ward in  about  every  five  or  six  hundred  feet  to  insure  accuracy, 
and  often  to  avoid  obstruction  in  line.  The  mode  of  proceeding  in 
such  cases  may  be  illustrated  with  the  deflections  of  the  2°  curve. 

The  instrument  in  the  first  place  is  set  at  station  501.148  and  the 
deflection  from  tangent  to  station  507  is  5°  51'.  Now  change  the 
position  of  the  instrument  to  station  507,  and  bring  the  cross  hairs 
to  bear  on  the  staff  at  station  501.148 ;  after  clamping  the  instru- 
ment turn  with  the  vernier  as  a  test 

for  station  502,  0°51' 

for      "       503,  1°51' 

for      "        504,  2°51' 

for      "        505,  3°51' 

and  for  the  tangential  station  507?  5°51'    *  Ch.  pt. 

If  the  stakes  are  found  to  be  correct,  continue  the  setting  of  the 
remaining  stakes  to  end  of  curve,  and  deflect  the  degrees  from  the 
beginning  of  curve  given  in  the  field  notes  opposite  the  respective 
stations. 

When  an  odd  number  of  minutes  are  to  be  turned  off  at  the 
commencement  and  for  each  successive  station,  the  inconvenience 
may  be  obviated  by  setting  the  vernier  the  number  of  minutes  for 
the  required  chord  in  an  opposite  direction  from  that  in  which  you 
would  turn  for  the  stations  in  the  curve ;  or  so  that  the  instrument 
when  set  in  line  with  the  tangent  and  clamped,  the  nonius  instead 
of  reading  0,  will  indicate  the  number  of  degrees  or  minutes  which 
would  be  deflected  to  strike  in  line  with  the  first  stake  to  be  set 
in  the  curve.  Then  the  remainder  of  the  stations  will  be  free  from 
the  odd  minutes  which  would  otherwise  be  turned  off  for  each 
successive  station. 

When  the  instrument  is  moved  forward  to  another  station,  the 
same  mode  may  be  adopted  with  reference  to  setting  the  nonius 
preparatory  to  bringing  the  cross  hairs  to  bear  on  the  staff  at  the 
beginning  of  curve. 

By  determining  the  tangents  at  the  various  points  in  the  curve 
over  which  the  instrument  may  be  set,  the  staking  of  the  curve 
may  be  prosecuted  with  Jess  liability  to  error. 


RAILROAD    CURVES. 


11 


At  the  end  of  curve  the  instrument  should  be  set  over  the  stake 
to  ascertain  if  the  tangent  produced  from  deflection  corresponds 
with  the  course  and  direction  of  the  tangential  line. 

FIELD  NOTES  AND  METHOD  OF  STAKING  A30  CURVE. 

Bearing  of  1st  tangent,  N.  20°  W. 
2d  N.  40°  W. 

Angle  of  deflection  by  needle  20°. 
"  "       by  graduated  card  20°. 


Station 


.  506.180    intersection  of  tangents. 

3.368    from  do.         do.  to  beginning  of  curve. 


k    Station  .    .  502.812    point  at  which  the  curve  commences. 
4-     6.666    length  of  curve. 


*    Station  .    .  509.478    point  at  which  the  curve  terminates. 


The  notes  are  put  down  as  represented  in  this  diagram,  and 
numbered  from  right  to  left  when  curving  to  the  left,  and  from 
left  to  right  when  curving  to  the  right. 


12 


EAILBOAD    CUKVES. 
FIELD    NOTES. 


Length 

Course  of 

Deflect'n 

No.  of 
Station 

chords. 

tangents 
and  chords. 

from 
tangent. 

BEMABKS. 

502.812 

«    c< 

N  20°  W 

0°    0' 

*  B.  C.  3°  to  left. 

503. 

18.8 

20°  17' 

0°17' 

504. 
505. 
506. 
507. 

100 
100 
100 
100 

22.04 
25.  04 
28.04 
31.  04 

1.47 
3.  17 
4.47 
6.  17 

*  Change  point. 

508. 

100 

34.  04 

7  47 

509. 
509.478 

100 
47.8 

37.  04 
29.04 

9.17 
10.  00 

*  E.  C. 

510. 

52.2 

N  40°  00  W 

The  number  at  which  the  curve- ends  should  be  given  to  the 
chainman  before  proceeding  to  measurement,  so  that  the  proper 
signal  may  be  made  by  him  on  arriving  at  the  station  next  preced- 
ing the  termination  of  the  curve. 

Then  set  the  instrument  over  the  point  of  curve  at  station  502.812 
and  deflect  from  the  tangent  line  for  station  503,  0°  17' 

504,  1°47' 

505,  3°  17' 

and  so  on  to  the  end  of  curve  as  per  column  of  deflection,  unless 
the  instrument  is  moved  forward.  If  it  is  necessary  to  move  the 
instrument,  then  set  it  over  another  stake  in  the  curve,  bring  the 
cross  hairs  to  bear  on  the  staff  at  the  beginning  of  curve  and 
clamp  the  instrument ;  then  turn  off  for  the  tangent  at  the  sta- 
tion selected,  the  same  number  of  degrees  originally  turned  from 
tangent  at  beginning  of  curve  in  setting  the  stake,  and  1°  30'  addi- 
tional for  each  successive  station  of  100  feet  as  you  advance ;  the 
angles  should  correspond  with  those  given  in  the  column  of  deflec- 
tions set  opposite  the  respective  stations. 

;*It  frequently  occurs  that  the  instrument  has  to  be  changed  to 
points  intermediate  between  two  stations. 

If  in  a  five  degrees  curve,  for  instance,  it  is  necessary  to  change 
the  instrument  from  station  No.  0,  there  being  an  obstruction  in 


KAILKOAD    CUEVES.  13 

the  line  of  sight  between  station  0  and  station  No.  3.  and  nothing 
to  prevent  the  instrument  being  set  over  a  point  in  the  curve  30 
feet  distant  from  station  2;  the  deflections  would  be  made  as 
follows : 

Station    0    Deflection  =  0°  00  B.  C.  5°  E. 

1  "  2°  30. 

2  "  5°  00. 

2.30       "  5°  45.  *    Change  point. 

Then  move  the  instrument  forward,  and  set  it  over  station  2.30, 
and  bring  the  cross  hairs  to  bear  on  the  staff  at  the  beginning  of 
the  curve,  station  0;  then  turn  off  5°  45'  for  tangent  at  station 
2.30  and  1°  45'  for  70  feet  the  remainder  of  station  No.  3,  making 
in  all  for  station  No  3— deflections  7°  30' 

4  "         10°  00' 

5  "         15°  00'  E.  C. 

The  angles  for  parts  of  a  station  on  curves  may  be  readily  calcu- 
lated and  the  angles  turned  off  in  such  manner  as  will  keep  the 
stations  of  uniform  length  throughout  the  line. 

REVERSE  CURVES. 

These  may  be  put  in  according  to  the  formation  of  the  ground 
with  equal  radii,  or  not,  as  the  case  may  require.  In  the  latter 
case  the  degree  of  curve  may  be  assumed  and  the  curve  continued 
as  far  as  deemed  necessary ;  and  the  tangent  is  then  produced  to 
the  intersection  and  measured — and  the  angle  of  deflection  de- 
termined. These  give  the  data  from  which  the  radius  and  degree 
of  curve  are  determined. — See  Pages  6  and  7. 

In  the  former  case  select  a  point  in  one  of  the  tangents  and  turn 
from  tangent  such  angle  as  the  case  may  require,  and  measure  on 
this  line  the  distance  between  the  tangents.  Then  set  in  a  point 
one  half  of  this  distance  for  the  point  of  reversion,  from  which  both 
curves  may  be  staked  out. — See  Pages  6  and  7.  » 

If  you  wish  to  compound  a  curve  so  that  the  trains  will  pass  less 
abruptly  from  tangent  into  and  through  the  curve,  it  may  be, 
done  in  the  following  manner ; 


14 


BAILKOAD    CUBVES. 


We  will  assume  the  angle  of  deflection  to  be  40° ;  in  the  tables 
under  40°  and  opposite  0'  find  2085.55,  the  distance  from  intersec- 
tion of  tangents  to  beginning  of  a  one  degree  curve. 

If  you  wi  h  to  lay  out  a  compound  equivalent  to  a  curve  of  5° 
for  the  whole  angle,  divide  the  distance  found  (2085.55)  by  5,  de- 
gree of  the  curve ;  and  you  have  the  point  of  beginning  417  ft.  from 
intersection  of  tangents.  You  will  then  decide  on  what  length  to 
substitute  the  less  degree  of  curve. 

Tf  a  3°  curve  is  decided  on,  and  the  distance  200  feet  at  each  end 
of  the  5°  curve,  then  deduct  3°  for  each  station  of  100  feet,  making 


EAILEOAD    CURVES, 


15 


12°  from  the  total  angle  of  deflection,  (40°)  and  you  have  28°  to  be 
divided  equally  between  the  stations  of  the  intermediate  curve,  or 
\B  =  7°,  the  required  degree  of  curve. 

FIELD  NOTES. 


No.  of 
Station. 

Course  of 
chords. 

Deflection. 

REMARKS. 

No  0. 

0°  00' 

Beginning  of  curve, 

1 

N  1°  30'  W 

1°  30' 

2 

4    30 

3    00 

End  of  curve,  3°,  B.  C.  7° 

3 

9    30 

3     30 

From  tangent. 

4 

16    30 

7    00 

5 

28    30 

10     30 

6 

30    30 

14    00 

E.  C.  7°,  B.  C.  3°. 

7 

35    30 

1    30 

From  tangent. 

8 

38    30 

3     00 

E.  C.  3°. 
Tangent,  N  40°  W. 

NATURAL    TANGENTS. 

From  the  tables  may  also  be  determined  the  natural  tangent  for 
any  given  number  of  degrees  and  minutes  from  one  degree  to  45°, 
by  taking  the  distance  given  in  the  tables  for  twice  the  angle  of 
which  the  tangent  is  sought,  and  dividing  the  same  by  5730. 

EXAMPLES  : 

1st.  Eequired  the  natural  tangent  of  30°.  Uncier  60°  (twice  the 
angle)  find  in  the  tables  3308.21  and  divide  the  same  by  5730,  and 
you  have  the  natural  tangent  for  30°  =  0.57735. 


2d.    Eequired  the  natural  tangent  for  an  angle  of  7°  28' ;  in  the 


16  RAILROAD    CURVES. 


column  of  distances  under  14°  and  opposite  56'  (twice  the  angle)  find 
750.97,  which  divided  by  5730  give  the  natural  tangent  for  7°  28' 
equal  to  0.13106. 

MEASUREMENT    WITH    GUNTEB'S    CHAIN. 

When  a  66  feet  chain  is  used  for  the  length  of  stations,  the  radius 
of  a  one  degree  curve.  5730  feet,  may  represent  57.30  chains  of  66 
feet,  and  the  distances  in  the  tables  applied  the  same  as  for  chains 
of  100  feet  in  length ;  but  the  radius  as  well  as  the  length  of  sta- 
tions will  be  proportionally  less  than  for  stations  of  100  feet  in 
length  by  3^  part. 

If  a  66  feet  chain  is  used,  the  distance  after  being  found  in  the 
tables,  may  be  divided  by  66,  and  the  stations  in  the  curve  reduced 
to  75.76  links  which  are  equal  to  50  feet,  one  half  the  length  of 
the  stations  generally  adopted  in  staking  the  center  line  of  rail- 
roads ;  and  the  curve  staked  out  accordingly,  turning  off  one  half 
the  number  of  degrees  required  for  the  stations  of  100  feet  in 
length. 

The  degree  of  curvature  is  understood  to  express  the  number  of 
degrees  per  100  feet,  and  hence  the  convenience  of  making  the  sta- 
tions of  such  length  as  will  give  a  definite  idea  of  the  degree  of 
curve  and  length  of  radius. 


The  following  abbreviations  are  used  by  some  Engineers. 

P.  C.        For  Point  of  Curve,  or  Beginning  of  Curve. 
P.  T.          "        "      "    Tangent,  or  End  of  Curve. 

P.  C.  C.  "  "  "  Compound  Curve— or  end  of  one  curve  and 
beginning  of  another,  curving  in  the  same 
direction. 

P.  E.  C.  «*  "  "  Reverse  Curve,  or  point  where  the  direction 
of  the  curve  is  changed  from  right  to  left, 
or  vice  versa. 

P.  I.         "       "     "    Intersection  of  Tangents. 


RAILROAD  CURVE  TABLES 


18 


RAILROAD  CURVE  TABLES. 

t 

0° 

1° 

2°            3° 

4° 

5° 

6° 

7° 

8° 

/ 

0 

0.00 

50.02 

10'XOO 

150.07 

200.09 

250.17 

300.30 

350.44 

400.70 

0 

1 

0.83 

50.85 

100.83 

150.90 

200.92 

251.00 

301.14 

351.28 

401.54 

1 

2 

1.67 

51.69 

101.67 

151.74 

201.76 

251.84 

301.97 

352.11 

402.37 

2 

8 

2.50 

52.52 

102.50 

152.57 

202.59 

252.67 

302.80 

352.95 

403.21 

3 

4 

3.33 

53.35 

103.34 

153.41 

203.43 

253.51 

303.64 

353.79 

404.05 

4 

5 

4.17 

54.18 

104.17 

154.24 

204.26 

254.34 

304.47 

354.62 

404.88 

5 

6 

5.00 

55.02 

105.01 

155.08 

205.10 

255.18 

305.31 

355.46 

405.72 

6 

7 

5.83 

55.85 

105.84 

155.91 

205.93 

256.01 

306.14 

356.30 

406.55 

7 

8 

6.67 

56.68 

106.68 

156.75 

206.77 

256.85 

306.98 

357.13 

407.39 

8 

9 

7.50 

57.52 

107.51 

157.58 

207.60 

257.68 

307.81 

357.97 

408.23 

9 

10 

8.33 

58.35 

108.35 

158.42 

208.44 

258.52 

308.65 

358.81 

409.06 

10 

11 

9.17 

59.18 

109.18 

159.25 

209.27 

259.35 

309.48 

359.64 

409.90 

11 

12 

10.00 

60.01 

110.02 

160.09 

210.11 

260.20 

310.32 

360.48 

410.74 

12 

13 

10.83 

60.85 

110-85 

160.92 

210.94 

261.03 

311.15 

361.32 

411.57 

13 

14 

11.67 

61.68 

111.69 

161.76 

211.77 

261.86 

311.99 

362.15 

412.41 

14 

15 

12.50 

62.52 

112.52 

162.59 

212.61 

262.70 

312.83 

362.99 

413.25 

15 

16 

13.33 

63.35 

113.36 

163.43 

213.45 

263.54 

313.66 

363.83 

414.08 

16 

17 

14.17 

64.18 

114.19 

161.26 

214.28 

264.37 

314.49 

364.66 

414.92 

17 

18 

15.00 

65.01 

115.02 

165.09 

215.11 

265.20 

315.33 

365.50 

415.75 

18 

19 

15.83 

65.85 

115.86 

165.93 

215.95 

266.04 

316.16 

366.34 

416.59 

19 

20 

16.67 

66.68 

116.69 

166.76 

216.78 

266.87 

317.00 

367.17 

417.43 

20 

21 

17.50 

67.51 

117.53 

167.60 

2x7.62 

267.71 

317.84 

368.01 

418.26 

21 

22 

18.33 

68.35 

118.36 

168.43 

218.45 

268.54- 

318.67 

368.85 

419.10 

22 

23 

19.17 

69.18 

119.20 

169.27 

219.29 

269.38 

319.50 

369.68 

419.94 

23 

24 

20.00 

70.01 

120.03 

170.10 

220.12 

270.21 

320.34 

370.52 

420.77 

24 

25 

20.83 

70.85 

120.87 

170.94 

22096 

271.05 

321.18 

371.36 

421.61 

25 

26 

21.67 

71.68 

121.70 

171.77 

221  79 

271.88 

322,01 

372.19 

422.45 

26 

27 

22.50 

72,51 

122.54 

172.61 

222.63 

272.72 

322.85 

373.03 

423.28 

27 

28 

23.33 

73.34 

123.37 

173.44 

223.46 

273.54 

323.68 

373.86 

424.1-2 

28 

29 

24.17 

74.18 

124.21 

174.28 

224.30 

274.38 

324.52 

374.70 

424.95 

.29 

30 

2500 

75.01 

125.03 

175.10 

225.13 

275.21 

325.35 

37554 

425.79 

30 

31 

25.83 

75.84 

125.87 

175.88 

225.96 

276.05 

326.19 

376.38 

426.63 

31 

32 

26.67 

76.68 

126.70 

176.72 

226.80 

276.88 

327.02 

377.22 

427.47 

32 

33 

27.50 

77.51 

127.53 

177.55 

227.63 

277.72 

327.86 

378.05 

428.31 

33 

34 

28.33 

*78.34 

128.37 

178.39 

22847 

278.55 

328.69 

378.89 

429.15 

34 

35 

29.17 

79.17 

129.20 

179.22 

229.30 

279.39 

329.53 

379.73 

429.98 

35 

36 

30.00 

80.01 

130.04 

180.06 

230.14 

280.23 

330.37 

380.57 

430.82 

36 

37 

30.83 

80.84 

130.87 

180.89 

230.97 

281.06 

331.20 

381.41 

431.66 

37 

38 

31.67 

81.67 

131.71 

181.73 

231.81 

281.90 

332.04 

382.24 

432.50 

38 

39 

32.50 

82.51 

132.54 

182.56 

232.64 

282.73 

332.87 

383.08 

433.34 

39 

40 

33.33 

83.34 

133.38 

183.40 

233.48 

283.57 

333.71 

383.92 

434.18 

40 

41 

34.17 

84.17 

134.21 

184.23 

234.31 

284.41 

334.55 

384.76 

435.02 

41 

42 

35.00 

85.01 

135.05 

185.07 

235.15 

285.24 

335.38 

385.60 

435.86 

42 

43 

35.83 

85.84 

135.88 

185.90 

235.98 

286.08 

336.22 

386.43 

436.70 

43 

44 

36.66 

86.67 

136.72 

186.74 

236.82 

286.91 

337.05 

387.27 

437.54 

44 

45 

37.50 

87.51 

137.55 

187.57 

237.65 

287.75 

337.89 

388.11 

438.37 

45 

46 

38.33 

88.34 

138.38 

188.40 

238.48 

288.59 

338.73 

388.95 

439.21 

46 

47 

39.17 

89.17 

139.22 

189.24 

239.32 

289.42 

339.56 

389.79 

440.05 

47 

48 

40.00 

90.00 

140.05 

190.07 

240.15 

290.26 

340.40 

390.62 

440.89 

48 

49 

40.83 

90.84 

140.89 

190.91 

240.99 

291.09 

341.23 

391.46 

441.73 

49 

50 

41.67 

91.67 

14172 

191.74 

241.82 

291.93 

342.07 

392.30 

442.57 

50 

51 

42.50 

92.50 

142.56 

192.58 

242,66 

292.77 

342.91 

393.14 

443.41 

51 

52 

43.33 

93.34 

143.39 

193.41 

243.49 

293.60 

343.74 

393.98 

444.25 

52 

53 

44.17 

94-17 

144.23 

194.25 

244.33 

294.44 

344.58 

394.81 

445.09 

53 

54 

45.00 

95.00 

145.06 

195.08 

245.16 

295.27 

345.41 

395.65 

445.93 

54 

55 

45.83 

95-84 

145.90 

195,92 

246.00 

296.11 

346.25 

396.49 

446.76 

55 

56 

46.67 

9ti.67 

146.73 

196.75 

246.83 

296.95 

347.08 

397.33 

447.60 

56 

57 

47.50 

97.50 

147.57 

197.59 

247.67 

297.78 

347.92 

398.17 

448.44 

57 

58 

48.33 

98.33 

148.40 

198.42 

248.50 

298.62 

348.76 

399.01 

449.28 

58 

69 

49.17 

99.17 

149.24 

199.26 

249.34 

299.46 

349.60 

399.85 

450.12 

59 

19 


RAILROAD  CURVE  TABLES. 

; 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

/ 

0 

450-95 

501.32 

551.74 

602.22 

652.87 

703.53 

754.35 

805.29 

856.35 

0 

1 

451.79 

502.16 

552.58 

603.06 

653.71 

704.38 

755.20 

806.14 

857.20 

1 

2 

452.63 

503.00 

553.42 

603,91 

654.56 

705.23 

75605 

806.99 

858.05 

2 

3 

453.47 

503.84 

554/26 

604.75 

655.40 

706.07 

756.89 

807.84 

858.90 

3 

4 

454.31 

504.68 

555.10 

605.60 

656.25 

706.92 

757.74 

808.64 

859.76 

4 

5 

455.14 

505.52 

555.94 

606.44 

657.09 

707.7.7 

758.59 

809.54 

860.61 

5 

6 

455.98 

506.36 

556.78 

607.28 

657.93 

708.62 

759.44 

810.39 

861.46 

6 

7 

456.82 

507.  '20 

557.62 

608.13 

658.78 

709.47 

760.29 

811.24 

862.31 

7 

8 

457.66 

508.04 

558.46 

608.97 

659.62 

710.31 

761.13 

812.09 

863.16 

8 

9 

458.50 

508.88 

559.30 

609.82 

660.47 

711.16 

761.98 

812.94 

864.01 

9 

10 

459.34 

509.72 

560.14 

610,66 

661.31 

712.01 

762.83 

813.79 

864.87 

10 

11 

460.18 

510  56 

560.98 

611.50 

6(52.15 

712.86 

763.68 

814.64 

865.72 

11 

12 

461.02 

511.40 

561.82 

612.35 

663.00 

713.71 

7(54.53 

815.49 

866.57 

12 

13 

461.86 

512.24 

562.66 

613.19 

663.84 

714.55 

765.37 

816.34 

867.42 

13 

14 

462.70 

513.08 

563.50 

614.04 

664.69 

715.40 

766.22 

817.19 

868.27 

14 

15 

463.53 

513.92 

564.34 

614.88 

665.53 

716.25 

767.07 

818.04 

869.12 

15 

16 

464.37 

514.76 

565.18 

615.72 

6(56.37 

717.10 

767.92 

818.89 

869.98 

16 

17 

465.21 

515.60 

566.02 

616.57 

667.22 

717.95 

768.77 

819.74 

870.83 

17 

18 

406.05 

516.44 

566.86 

617.41 

6t>8.06 

718.79 

769.61 

82059 

871.68 

18 

19 

466.89 

517.28 

567.70 

618.26 

668.91 

719,64 

770.46 

821.44 

872.53 

19 

20 

467.73 

518.12 

568.54 

619.10 

669.75 

720.49 

771.31 

822  29 

873.38 

20 

21 

468.57 

518.96 

569.38 

619.94 

670.59 

721.35 

772.16 

823.14 

874.23 

21 

22 

469.41 

51980 

570.22 

620.79 

671.44 

722.20 

773.01 

823  99 

875.09 

22 

23 

470.25 

520.64 

571.06 

021.63 

672.28 

723.04 

773.85 

824.84 

875.94 

23 

24 

471.08 

521.48 

571.90 

622.48 

673.13 

723.89 

774.70 

825  69 

876.79 

24 

25 

471.92 

522.32 

572.74 

623.32 

673.97 

724.74 

775.55 

826.54 

877.64 

25 

26 

472.76 

523.16 

573.58 

624.16 

674.81 

725.59 

776.40 

827.39 

878.49 

26 

27 

473.60 

524.01 

574.42 

625.01 

675.66 

726.44 

777.35 

828.24 

879.34 

27 

28 

474.43 

524.85 

575.27 

625.85 

676.51 

727.28 

778.09 

82909 

880.20 

28 

29 

475.26 

525.69 

576.11 

626.70 

677.35 

728.13 

778.94 

829.94 

881.05 

29 

30 

476.10 

526.53 

576.95 

627.55 

678.20 

7'28.97 

779.79 

830.79 

881.90 

30 

31 

476.94 

527.37 

577.79 

6'28.39 

679.04 

729.82 

780.64 

831.64 

882.75 

31 

32 

477.78 

528.21 

578.63 

629.24 

679.89 

730.66 

781.49 

832.49 

883.61 

32 

33 

478.62 

529.05 

579.48 

630.08 

680.73 

731.51 

782.34 

833.35 

884.46 

33 

34 

479.46 

529.89 

580.32 

630.93 

681.58 

732.35 

783.19 

834.20 

885.32 

34 

35 

480.30 

530.73 

581.16 

631.77 

682.42 

733.20 

784.04 

835.05 

886.17 

35 

36 

481.14 

531.57 

582.00 

632.61 

683.26 

734.05 

784.89 

835.90 

887.02 

36 

37 

481.99 

532.41 

582.84 

633  46 

684.11 

734.89 

785.74 

836.75 

887.88 

37 

38 

482.83 

533.25 

583.69 

634.30 

684.95 

73.").74 

786.59 

837.61 

888.73 

38 

39 

483.67 

534.09 

5H4.53 

635.15 

685.80 

736.58 

787.44 

838.46 

889.59 

39 

40 

484.51 

534.93 

585.37 

635.99 

686.64 

737.43 

788/29 

839.31 

890-44 

40 

41 

485.35 

535.77 

586.21 

636.83 

687.48 

738/28 

789.14 

840.16 

891.29 

41 

42 

486.19 

536.61 

587.05 

637.68 

688.33 

739.12 

789.99 

841.01 

89-'.  15 

42 

43 

487.03 

537.45 

587.90 

638.52 

689.17 

739.97 

790.84 

841.87 

893.00 

43 

44 

487.87 

538.29 

588.74 

639.37 

690.02 

740.81 

791.69 

842.72 

893.86 

44 

45 

488.71 

539.13 

589.58 

640.21 

690.86 

741.66 

792.54 

843.57 

894.71 

45 

46 

48956 

539.97 

590.42 

641.05 

691.70 

742.51 

793.39 

8,14.42 

89551 

46 

47 

490.40 

540.81 

591.26 

641.90 

692.55 

743.35 

794.24 

845.27 

896.42 

47 

48 

491.24 

511.65 

592.11 

642.74 

693.89 

744.20 

795.09 

846.13 

897.27 

48 

49 

492.08 

542.49 

592.95 

643.59 

694.24 

745.04 

795.94 

846.98 

898.13 

49 

50 

492.92 

543.33 

593.79 

644.43 

695.08 

745.89 

796.79 

847.83 

898.98 

50 

51 

493.76 

541.17 

594.03 

645.27 

695.92 

746.74 

797.64 

848.  6S 

899.83 

51 

52 

494.60 

545.01 

595.47 

646.12 

696.77 

747.58 

798.49 

849.53 

900.69 

52 

53 

495.44 

545.85 

596.32 

646.96 

697.61 

748.43 

799.34 

P50.39 

901.54 

53 

54 

496.28 

546.69 

597.16 

647.81 

69846 

749.27 

800.19 

851.24 

902.40 

54 

55 

497.12 

547.53 

598.00 

648.65 

699.30 

750.12 

801.04 

852.09 

903.25 

55 

56 

497.96 

548.37 

598.84 

649.49 

70014 

750.97 

801.89 

852.94 

904.10 

56 

57 

498.H1 

549.21 

599.68 

650.34 

700.99 

751.81 

802.74 

853.79 

904.96 

57 

58 

499.65 

550.06 

600.53 

651.18 

701.83 

752.66 

803.59 

854.65 

905,81 

58 

59 

500.48 

550.90 

601.38 

652.03 

702.68 

753.50 

804.44 

855.50 

906.67 

59 

20 


RAILROAD  CURVE  TABLES. 

r 

18° 

19° 

20°  |  21°  |  22°  1  23°  |  24° 

25°  |  26° 

/ 

0 

907.52 

958.86  '  1010.37  :  1062.00  1113.80 

1165.76 

1217.96  i  1270.28 

1322.88 

0 

1 

908.38 

959.72 

1011.23  i  1062.86 

1114.67 

1166.63 

1218.83  1271.16 

1323.76 

1 

2 

90J.23 

960.57 

1012.09 

1063.73 

1115.53 

1167.50 

1219.70 

1272.03 

1324.63 

2 

3 

910.09 

961.43 

1012.95 

1064.59 

1116.40 

1168.37 

1220.57 

1272.91 

1325.51 

3 

4 

910.94 

962.30 

1013.81 

1065.45 

1117.26 

1169.24 

1221.45 

1273.79 

1326.39 

4 

5 

911.80 

963.15 

1014.67 

1066.32 

1118.13 

1170.11 

1222.32 

1274.66 

1327.27 

5 

6 

912.65 

964.00 

1015.53 

1067.18 

1118.99 

1170.98 

1223.19 

1275.54 

1328.14 

6 

7 

913.51 

964.86 

1016.39 

1068.04 

1119.86 

1171.85 

1224.06 

1276.42 

1329.02 

7 

8 

914.36 

965.72 

1017.24 

1068.91 

1120.72 

1172.71 

1224.93 

1277.29 

1329.90 

8 

9 

915.22 

966.58 

1018.10 

1069.77 

1121.59 

1173.58 

1225.80 

1278.17 

1330.78 

9 

10 

916.07 

967.43 

1018.96 

1070.63 

1122.45 

1174.45 

1226.67 

1279.05 

1331.65 

10 

11 

916.93 

968.29 

1019.82 

1071.50 

1123.32 

1175.32 

1227.54 

1279.92 

1332.53 

11 

12 

917.78 

969.15 

1020.68 

1072.36 

1124.18 

1176.19 

1228.42 

1280.80 

1333.41 

12 

13 

918.64 

970.00 

1021.54 

1073.22 

1125.05 

1177.06 

1229.29 

1281.69 

1334.28 

13 

14 

919.49 

970.86 

1022.40 

1074.09 

1125.91 

1177.93 

1230.16 

1282.55 

1335-16 

14 

15 

920.35 

971.72 

1023.26 

1074.95 

1126.78 

1178.80 

1231.03 

1283.43 

1336.04 

15 

16 

921.20 

972.58 

1024.12 

1075.81 

1127.64 

1179.67 

1231.90 

1284.31 

1336.92 

16 

17 

922.06 

973.43 

1024.98 

1076.68 

1128.50 

1180.54 

1232.77 

1285.18 

1337.79 

17 

18 

922.91 

974.29 

1025.84 

1077.54 

1129.37 

1181.41 

1233.64 

1286.06 

1338.67 

18 

19 

923.77 

975.15 

1026.70 

1078.40 

1130.24 

1182.28 

1234.51 

1286.94 

1339.55 

19 

20 

924.63 

976.01 

1027.56 

1079.27 

1131.10 

1183.15 

1235.39 

1287.81 

1340.43 

20 

21 

925.48 

976.86 

1028.42 

1080.13 

1131.97 

1184.02 

1236.26 

1288.69 

1341.30 

21 

22 

926.34 

977.72 

1029.27 

1080.99 

1132.83 

1184.88 

1237.13 

1289.57 

1342.18 

22 

23 

927.19 

978.58 

1030.13 

1081.86 

1133.70 

1185.75 

1238.00 

1290.44 

1343.06 

23 

'24 

928.05 

979.44 

1030.99 

1082.72 

1134.56 

1186.62 

1238.87 

1291.32 

1343.94 

24 

25 

928.90 

980.29 

1031.85 

1083.58 

1135.43 

1187.49 

1239.74 

1293.20 

1344.81 

25 

26 

929.76 

981.15 

1032.71 

1084.45 

1136.29 

1188.36 

1240.61 

1293.07 

1345.69 

26 

27 

930.61 

982.01 

1033.57 

1085.31 

1137.16 

1189.23 

1241.49 

1293.95 

1346.57 

27 

•28 

931.47 

982.86 

1034.43  1086.17 

1138.02 

1190.10 

1242.36 

1294.83 

1347.44 

28 

29 

932.32 

983.72 

1035.29 

1087.04 

1138.89 

1190.97 

1243.23 

1295.70 

1348.32 

29 

30 

933.18 

984.58 

1036.15 

1087.90 

1139.75 

1191.84 

1244.10 

1296.58 

1349.20 

30 

31 

934.04 

985.44 

1037.01 

1088.76 

1140.62 

1192.71 

1244.97 

1297.46 

1350.08 

31 

32 

934.89 

986.30 

1037.87 

1089.63 

1141.48 

1193.58 

1245.85 

1298.33 

1350.96 

32 

33 

935.75 

987.16 

1038.74 

1090.49 

1142.35 

1194.45 

1246.72 

1299.21 

1351.85 

33 

34 

936.60 

988.02 

1039.60 

1091.35 

1143.22 

1195.32 

1247.59 

1300.09 

1352.73 

34 

35 

937.46 

988.88 

1040.46 

1092.22 

1144.09 

1196.19 

1248.46 

1300.96 

1353.61 

35 

36 

938.32 

989.74 

1041.32 

1093.08 

1144.95 

1197.06 

1249.34 

1301.84 

1354.49 

36 

37 

939.17 

990.60 

1042.18 

1093.94 

1145.82 

1197.93 

1250.21 

1302.72 

1355.37 

37 

38 

940.03 

991.46 

1043.05 

1094.81 

1146.69 

1198.80 

1251.08 

1303.59 

1356.25 

38 

39 

940.88 

992.32 

1043.91 

1095.67 

1147.55 

1199.68 

1251.95 

1304.47 

1357.14 

39 

40 

941.74 

993.18 

1044.77 

1096.53 

1148.42 

1200.55 

1252.83 

1305.35 

1358.02 

40 

41 

942.60 

994.04 

1045.63 

1097.40 

1149.29 

1201.42 

1253.70 

1306.22 

1358.90 

41 

42 

913.45 

994.90 

1046.49 

1098.26 

1150.15 

1202.29 

1254.57 

1307.10 

1359.78 

42 

43 

944.31 

995.76 

1047.36 

1099.12 

1151.02 

1203.16 

1255.44 

1307.98 

1360.66 

43 

44 

945.16 

996.62 

1048.22 

1099.99 

1151.89 

1204.03 

1256.32 

1308.85 

1361.54 

44 

-15 

946.03 

997.48 

1049.03 

1100.85 

1152.76 

1204.90 

1257.19 

1309.73 

1362.43 

45 

46 

946.88 

998.34 

1049.94 

1101.71 

1153.62 

1205.77 

1258.06 

1310.61 

1363.31 

46 

47 

947.73 

999.19 

1050.80 

1102.58 

1154.49 

1206.64 

1258.93 

1311.48 

1364.19 

47 

48 

948.59 

1000.95 

1051.67 

1103.44 

1155.36 

1207.51 

1259.81 

131-2.36 

136507 

48 

49 

919.44 

1000.91 

1052.53 

1104.30 

1156.22 

1208.38 

1260.68 

1313.24 

1365.95 

49 

50 

950.30 

1001.77 

1053.39 

1105.17 

1157.09 

1209.25 

1261.55 

1314.11 

1366.83 

50 

51 

951.16 

1002.63 

1054.25 

1106.03 

1157.96 

1210.12 

1262.42 

1314.99 

1367.72 

51 

5-2 

952.01 

1003.49 

1055.11 

1106.89 

1158.82 

1210.99 

1263.30 

1315.87 

1368.60 

52 

53 

952.87 

1004.35 

1055.98 

1107.76 

1159.69 

1211.86 

1264.17 

1316.74 

1369.48 

53 

54 

953.72 

1005.21 

1056.84 

1108.62 

1160.56 

1212.73 

1265.04 

1317.62 

1370.36 

54 

55 

954.58 

1006.07 

1057.70 

1109.48 

1161.43 

1213.61 

1265.92 

1318.50 

1371.24 

55 

56 

955.44 

1006.93 

1058.56 

1110.35 

1162.29 

1214.48 

1266.79 

1319.37 

1372.12 

56 

57 

956.29 

1007.79 

1059.42  1111.21 

1163.16 

1215.35 

1267.66 

1320.25  j  1373.01 

57 

58 

957.15 

1008.65  i  1060.28  1112,07 

1164.03 

1216.22 

1268.53  1321.13  i  1373.89 

58 

59 

958.00 

1009.51  .  1031.14  1112.94 

1164.89 

1217.09  1269.41  1322.00  1374.77 

59 

RAILROAD  CURVE  TABLES. 

i 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

e 

0 

1375.65 

1428.65 

1481.89  1535.30 

1589.04 

1643.08 

1697.28 

1751.S3 

1806.67 

0 

1 

1376.53 

1429.54 

1482.78 

1536.20 

1589.94 

1643.98 

1698.19 

175-2.74 

1807.59 

i 

2 

1377.41 

1430.42 

1483.67 

1537.09 

1590.84 

1644.88 

1699.10 

1753.66 

1808.50 

2 

3 

1378.30 

1431.31 

1484.56 

1537.99 

1591.74 

1645.78 

1700.01 

1754.57 

1809.42 

3 

4 

1379.18 

1432.20 

1485.45 

1538.88 

1592.64 

1646.69 

1700,92 

1755.48 

1810.34 

4 

5 

1380.06 

1433.08 

1486.34 

1539.78 

1593.54 

1647.59 

1701.83 

1756.40 

1811.25 

5 

6 

1380.94 

1433.97 

1487.23 

1540.67 

1594.44 

1648.49 

1702.74 

1757.31 

1812.17 

6 

7 

1381.82 

1434.86 

1488.12 

1541.57 

1595.34 

1649.39 

1703.65 

1758.22 

1813.09 

7 

8  138-2.70 

1435.74 

1489.01 

1542.47 

1596.24 

1650.29 

1704.55 

1759.13 

1814,00 

8 

9  1383.59 

1436.63 

1489.90 

1543.36 

1597.14 

1651.19 

1705.46 

1760.05 

1814.92 

9 

10  1384.47 

1437.52 

1490.79 

1544.26 

1598.04 

1652.09 

1706.37 

1760.96 

1815.84 

10 

11 

1385.35 

1438.40 

1491.68 

1545.15 

1598.94 

1652.99 

1707.28 

1761.87 

1816.75 

11 

12 

1386.23 

1439.29 

1492.57 

1546.05 

1599.84 

1653.90 

1708.19 

1762.79 

1817.07 

12 

13 

1387.11 

1440.18 

1493.46 

1546,94 

1600.74 

1654.80 

1709.10 

1763.70 

1818,59 

13 

14 

1387.99 

1441.06 

1494.35 

1547.84 

1601.64 

1655.70 

1710.01 

1764.61 

1819.50 

14 

15 

1388.88 

1441.95 

1495.24 

1548.74 

1602.54 

1656.60 

1710.92 

1765.53 

1820.42 

15 

16 

1389.76 

1442.84 

1496.13 

1549.63 

1603.44 

1657.50 

1711.83 

1766.44 

182134 

16 

17 

1390.64 

1443.72 

1497.02 

1550.53 

1604.33 

1658.40 

1712.74 

1767.35 

1822.25 

17 

18 

1391.52 

1444.61 

1497.91 

1551.42 

1605.23 

1659.30 

1713.65 

1768.26 

1823.17 

18 

19 

1392.40 

1445.50 

1498.80 

1552,32 

1006.13 

1660.20 

1714.56 

1769.18 

1824.09 

19 

20 

1393.28 

144(5.38 

1499.69 

1553.21 

1607.03 

1661.11 

1715.47 

1770.09 

1825.00 

20 

21 

1394.17 

1447.27 

1500.58 

1554.11 

1607.93 

1662.01 

1716.38 

1771.00 

1825.92 

21 

22 

1395.05 

1448.16 

1501.47 

1555.00 

1608.83 

1662.91 

1717.28 

1771.92 

1826.84 

22 

23 

1395.93 

1449.04 

1502.36 

1555.90 

1609.73 

1663.81 

1718,19 

1772.83 

1827.75 

23 

24 

1396.81 

1449.93 

1503.25 

1556.80 

1610.63 

1664.71 

1719.10 

1773.74 

1828.67 

24 

25 

1397.69 

1450,82 

1504.U 

1557.69 

1611.53 

1665.61 

1720.01 

1774.66 

1829.59 

25 

26 

1398.57 

1451.70 

1505,03 

1558.59 

1612.43 

1666.51 

1720.92 

1775.57 

1830.50 

26 

27 

1399.46 

1452.59 

1505.92 

1559.48 

1613.33 

1667.42 

1721.83 

1776.48 

1831.42 

27 

28 

1400.34 

1453.48 

1506.81 

1560-38 

1614.23 

1668.32 

1722.74 

1777.39 

1832.34 

28 

29 

1401.22 

1454  36 

1507.70 

1561.28 

1615.13 

1669.22 

1723.65 

1778.31 

1833.25 

29 

30 

1402.10 

1455.25 

1508.59 

1562.17 

1616.03 

1670.12 

1724.56 

1779.22 

1834.17 

30 

31 

1402.99 

1456.U 

1509.48 

1563.07 

1616.93 

1671.03 

1725.47 

1780.14 

1835.09 

31 

32 

1403.87 

1457.03 

1510.37 

1563.96 

1617.83 

1671.93 

1726.38 

1781.05 

1836.01 

32 

33 

1404.76 

1457.91 

1511.26 

1564.86 

1618.74 

1672.64 

1727.29 

1781.97 

1836.93 

33 

34 

1405.64 

1458.80 

1512.15 

1565.75 

1619.64 

1673.74 

1728.20 

1782.88 

1837.85 

34 

35 

140ti.53 

1459.69 

1513.04 

1566.65 

1620.54 

1674.65 

1729.10 

1783.80 

1838.77 

35 

36 

1407.41 

1460.58 

1513.93 

1567.54 

1621.44 

1675.55 

1730.01 

1784.71 

1839.69 

36 

37 

1408.30 

1461.47 

1514.82 

1568.44 

1622.34 

1076.46 

1730.92 

1785.63 

1840.61 

37 

38 

140SU8 

1462.35 

1515.71 

1569.34 

1623.24 

1677,36 

1731.83 

1786.54 

1841.54 

38 

39 

1410.07 

1463.24 

1516.60 

1570.23 

1624.15 

1678.27 

1732.74 

1787.46 

1842.46 

39 

40 

1410.95 

1464.13 

1517.49 

1571.13 

1625.05 

1679.17 

1733.65 

17H8.37 

1843.38 

40 

41 

1411.84 

1465,02 

1518.38 

1572.02 

1625.95 

1080.08 

1734.56 

1789.29 

1844.30 

41 

42 

1412.72 

1465.91 

1519.27 

1572.92 

1626.85 

1680.98 

1735.47 

1790.20 

1845.22 

42 

43 

1413.01 

1466.79 

1520.16 

1573.81 

1627.75 

1681.89 

1736.38 

1791.12 

1846.14 

43 

44 

1414.49 

1467.68 

1521.05 

1574.71 

1628.65 

1682.79 

1737.29 

1792.03 

1847.06 

44 

45 

1415.38 

1468.57 

1521.94 

1575.61 

1629.56 

1683.70 

1738.20 

1792.95 

1847.98 

45 

46 

1416.26 

1469.46  J1522.83 

1576.50 

1630.46 

1684.61 

1739.10 

1793.86 

1848,90 

46 

47 

1417.15 

1470.35 

1523.73 

1577.40 

1631.36 

1685.51 

1740.01 

1794.78 

1849.82 

47 

48 

1418.03 

1471.23 

1524.62 

1578.29 

1632.26 

1686.42 

1740.92 

1795.69 

1850.74 

48 

49 

1418.92 

1472.12 

1525.51 

1579.19 

1633.16 

1687.32 

1741.83 

1796.61 

1851.66 

49 

50 

1419.80 

1473.01 

1526.40 

1580.08 

1634.06 

1688.23 

1742.74 

1797.52 

1852.58 

50 

51 

1420.69 

1473.90 

1527.29 

1580.98 

1634.97 

1689.13 

1743.65 

1798.44 

1853.50 

51 

52 

1421.57 

1474.79 

1528.18 

1581.88 

1635.87 

1690.04 

1744.56 

1799,35 

1854.43 

52 

53 

1422.46 

1475.67 

1529.07 

1582.77 

1636,77 

1690.94 

1745.47 

1800.27 

1855.35 

53 

54 

1423.34 

1476.56 

1529.96 

1583.67 

1637.67 

1691.85 

1746.38 

1801.18 

1856,27 

54 

55 

1424.23 

1477.45 

1530.85 

1584.56 

1638.57 

1692.75 

1747,29 

1802.10 

1857.19 

55 

56 

1425.11 

1478.34 

1531.74 

1585.46 

1639.47 

1693.66 

1748.19 

1803.01 

1858.11 

56 

57 

1425.99 

1479.23 

1532.63 

1586.35 

1640.38 

1694.56 

1749.10 

1803.93 

1859.03 

57 

58 

1426.88 

1480.11 

1533.52 

1587.25 

1641.28 

1695.47 

1750.01 

1804.84 

1859.95 

58 

59 

1427.77 

1481.00 

1534.41  1588.15 

1642.18 

1696.37 

1750.92 

1805.76 

1860,87 

59 

22 


RAILROAD  CURVE  TABLES. 

/ 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

r 

0 

1861.79  1917.26  1973.01  2029.11 

2085.55  2142.33  2199.52  2257.10  2315.09   0 

1 

1862.71 

1918.19 

1973.94 

2030.05 

2086.50  2143.28 

2200.48  2258.06 

2316.06 

1 

2 

1863.64 

1919.11 

1974.88 

2030.99 

2087.44  ;  2144.24 

2201.44  1  2259.03 

2317.03 

2 

3 

1864.56 

1920.04 

1975.81 

2031.93  !  2088.39  !  2145.19 

2202.40 

2259.99 

2318.00 

3 

4 

1865.48 

1920.97 

1976.75 

2032.87 

2089.33 

2146.14 

2203.35 

2260.96 

2318.97 

4 

5 

1866.41 

1921.89 

1977.68 

2033.81 

2090.28 

2147.10 

2204.31 

2261.92 

2319.94 

5 

6 

1867.33 

1922.82 

1978.61 

2034.75 

2091.22 

2148.05 

2205.27 

2262.89 

2320.91 

6 

7 

1868.25 

1923.74 

1979.55 

2035.69 

2092.17 

2149.00 

2206.23 

2263.85 

2321.88 

7 

8 

1869.17 

1924.67 

1980.48 

2036.63 

2093.11 

2149.95 

2207.19 

2264.82 

2322.85 

8 

9 

1870.10 

1925.60 

1981.42 

2037.67 

2094.06  2150.91 

2208.15 

226578 

2323.82 

9 

10 

1871.02 

1926.52 

1982.35 

2038.51 

2095.00  |  2151.86 

2209.11 

2266.75 

2324.79 

10 

11 

1871.94 

1927.45 

1983.28 

2039.45 

2095.95  1  2152.81 

2210.07 

2267.71 

2325.76 

11 

12 

1872.86 

1928.38 

1984.22 

2040.39 

2096.89 

2153.77 

2211.02 

2268.68 

2326.73 

12 

13 

1873.78 

1929.30 

1985.15 

2041.33 

2097.84  2154.72 

2211.98  i  2263.64 

2327.70 

13 

14 

1874.71 

1930.23 

1986.09 

2042.27 

2098.78  !  2155.67 

2212.94 

2270.61 

3328.67 

14 

15 

1875.63 

1931.15 

1987.02 

2043.21 

2099.73 

2156.63 

2213.90 

2271.57 

2329.64 

15 

16 

1876.55 

1932.08 

1987.95 

2044.15 

2100.67 

2157.58 

2214.86 

2272.54 

2330.61 

16 

17 

1877.48 

1933.01 

1988.89 

2045.08 

2101.62 

2158  53 

2215.82 

2273.50 

2331.59  17 

18 

1878.40 

1933.93 

1989.82 

2046.02 

2102.57 

2159.48 

2216.78 

2274.46 

2332.56 

18 

19 

1879.32 

1934.86 

1990.76 

2046.96 

2103.51 

2160.44 

2217.74 

2275.43 

2333.52 

19 

20 

1880.24 

1935.79 

1991.69 

2047.90 

2104.46 

2161.39 

2218.69 

2276.39 

2334.49  20 

21 

1881.16 

1936.71 

1992.62 

2048.84 

2105.40 

2162.34 

2219.65  2277.36 

2335.46  21 

22 

1882.09 

1937.64 

1993.56 

2049.78 

2106.35 

2163.30 

2220.61  2278.32 

2336.44  22 

23 

1883.01 

1938.56 

1994.49 

2050.72 

2107.29 

2164.25 

2221.57  2279.29 

2337.41  23 

24 

1883.93 

1939.49 

1995.43 

2051.66 

2108.24  .2165.20 

2222.53 

2280.25 

2338.38  24 

25 

1884.86 

1940.42 

1996.36 

2052.60 

2109.18  2166.16 

2223.49 

2281  22 

2339.35  25 

26 

1885.78 

1941.34 

1997.29 

2053.54 

2110.13  2167.11 

2224.45 

2282.18 

2340.32  |  26 

27  1886.71 

1942.27 

1998.23 

2054.48 

2111.07  2168.06 

2225.40 

2283.15 

2341.29 

27  . 

28 

1887.63 

1943.20 

1999.16 

2055.42 

2112.02  2169.01 

2226.36 

2284.11 

2342.26 

28' 

29 

1888.55 

1944.12 

2000.10 

2056.36 

2112.96  2169.97 

2227.32 

2285.08 

2343.23  i  29 

30 

1889.47 

1945.05 

2001.03 

2057.30 

2113.91  2170.92 

2228.28 

2286.04 

2344.20" 

30 

31 

1890.40 

1945.98 

2001.97 

2058.24 

2114.86  ;  2171.87 

2229.24 

2287.01 

2345.17 

31 

32 

1891.32 

1946.91 

2002.90 

2059.18 

2115.80  ;  2172.83 

2230/20  2287.98 

2346.15  !  32 

33 

1892.25 

1947.85 

2003.84 

2060.13 

2116.75  2173.78 

2231.16  2288.94 

2347.12  |  33 

34 

1893.17 

1948.78 

2004.77 

2061.07 

2117.70  |  2174.73 

2232.12 

2289.91 

2348.10  i  34 

35 

1894.10 

1949.71 

2005.71 

2062.01 

2118.65  i  2175  69 

2233  08 

2290.88 

234907  35 

36 

1895.03 

1950.64 

2006.65 

2062.95 

2119.59  2176.64 

2234.04 

2291.85 

2350.04  36 

37 

1895.95 

1951.57 

2007.58 

2063.89 

2120.54  i  2177.59 

2235  00 

2292.82 

2351.02 

37 

38 

1896.88 

1952.51 

2008.52 

2064.83 

2121.49  i  2178.55 

2235.97 

2293.79 

2351.99 

38 

39 

1897.81 

1953.44 

2009.45 

2065.78 

2122.44 

2179.50 

2236.93 

2294.75 

2352.97 

39 

40 

1898.73 

1954.37 

2010.39 

2066.72 

2123.38 

21*0.45 

2237.89 

2295.72 

2353.94 

40 

41 

1899.66 

1955.30 

2011.33 

2067.66 

2124.33 

2181.41 

2238.85 

2296.69 

2354.91 

41 

42 

1900.59 

1956.23 

2012.26 

2068.60 

2125.28 

2182.36 

2239.81 

2297.66 

2355.89  42 

43 

1901.51 

1957.17 

2013.20 

2069.54 

2126.22 

2183.31 

2240.77 

2298.63 

235686  43 

44 

1902.44 

1958.10 

2014.34 

2070.48 

2127.17 

2184.27 

2241.73 

2299.60 

2357.84 

44 

45 

1903.36 

1959.03 

2015.07 

2071.43 

2128.12 

2185.22 

2242.69 

2300.56 

2358.81 

45 

46 

1904.29 

1959.96 

2016.01 

2072.37 

2129.07 

2186.17 

2243.65 

2301.53 

2359.78  46 

47 

1905.22 

1960.89 

2016.94 

2073.31 

2130.01 

2187.13 

2244.61 

2302.50 

236076  47 

48 

1906.14 

1961.83 

2017.88 

2074.25 

2130.96 

2188.08 

2245.57 

230347 

2361.73 

48 

|49 

1907.07 

1962.76 

2018.81 

2075.19 

2131.91 

2189.03 

2246.53 

2304.44 

2362.71  49 

150 

1908.00 

1963.69 

2019.75 

2076.13 

2132.86  2189.99 

2247.49 

2305.41 

2363.68  !  50 

!51 

1908.92 

1964.62 

2020.69 

2077.08 

2133.80  2190.94 

2248.45 

2306.37 

2364.65  51 

i52 

1909.85 

1965.55 

2021.62 

2078.02 

2134.75  2191.89 

2249  42 

2307.34 

2365.63  !  52 

153 

1910.77 

1966.49 

2022.56 

2078.99 

2135.70 

2192.85 

2250.38 

2308  31 

23('6.60  53 

54 

1911.70 

1967.42 

2023.49 

2079.90 

2136.65 

2193.80 

2251.34 

2309.28 

2367.58  54 

55 

1912.63 

1968.35 

2024.43 

2080.84 

2137.59 

2194.75 

2252.30 

2310.25 

2368.55  55 

56 

1913.55 

1969.28 

2025.37 

2081.78 

2138.54 

2195.71 

2253.26 

2311.22 

2369.52  56 

57 

1914.48 

1970.21 

2026.30 

2082.73 

2139.49 

2196.66 

2254.22 

2312.18 

2370.50 

57 

58 

1915.41 

1971.15 

2027.24 

2083.67 

2140.43 

2197.61 

2255.18 

2313.15 

2371.47 

58 

59 

1916.33 

1972.08 

2028.17 

2084.61 

2141.38 

2198.57 

2256.14  2314.21 

2372.45 

59 

23 


RAILROAD  CURVE  TABLES. 

/ 

45° 

46° 

47° 

48° 

49°  |  50° 

51° 

52°   |  53° 

t 

0 

2373.42 

2432.21 

2491.46 

2551.11 

2611.27 

2671.90  •  2733.04 

2794.69 

2856.86 

0 

1 

2374.40 

2433.20 

2492.45 

2552.11 

2612.28 

2672.92  2734.07 

2795.72 

2857.90 

1 

U 

28  i  5.  38 

2434.18 

2493.45 

2553.11 

26  1  3.29 

2673.94  2735.09 

2796.76 

2858.95 

2 

3 

2376.35 

2435.17 

2494.44 

2554.11 

2614.30 

2674.95  1  2736.12 

2797.79 

2859.99 

3 

.  4 

2377.33 

2436.15 

2495.43 

2555.11 

2615.31 

2675.97  2737.14 

2798.82 

2861.03 

4 

i  5 

2378.31 

2437.14 

249*6.43 

2556.11 

2616.32 

2676.99 

2738.17 

2799.86 

2862.08 

5 

6 

2379.29 

2438.12 

2497.42 

2557.12 

2617.32 

2678.01 

2739.19 

280J.89 

2863.12 

6 

7 

2380/27 

2439.11 

2498.41 

2558.12 

2618,33 

267903  '/740.22 

2801.92 

2864.16 

7 

8 

2381.24 

2440.10 

2469.40 

2559.12 

2619.34 

2680.04  2741.25 

2802.96 

2865.20 

8 

9 

2382.22 

2441.08 

2500.40 

2560.12 

2620.35 

2681.06 

2742.27 

2803.99 

2866.25 

9 

10 

2383.20 

2442.07 

2501.39 

2561.12 

2621.36 

2682.08 

2743.30 

2805.02 

2867.29 

10 

11 

2384.18 

2443.05 

2502.38 

2562.12 

2622.36 

2683.10 

!  2744.32 

2806.06 

2868.33 

11 

12 

2385.16 

2444.04 

2503.38 

2563.12 

2623.37 

2684.12 

2745.35 

2807.09 

2869.38 

12 

13 

2386.13 

2445.02 

2504.37 

2564.12 

2624.3S 

2685.13 

2746.37 

2808.12 

2870.42 

13 

14 

2387.11 

2446.01 

2505.36 

2565.12 

2625.39 

2686.15 

2747.40 

2809.16 

2871.46 

14 

15 

2388.09 

2447.00 

2506.36 

2566.12 

2626.40 

2687.17 

2748.43 

2810-19 

2872.51 

15 

36 

2389.07 

2447.98 

2507.35 

2567.13 

2627.41 

26«8.19 

2749.45 

2811.22 

2873.55 

16 

!  17 

2390.05 

2448.97 

2508.34 

2568.13 

2628.41 

2689.21 

2750.48 

2812.26 

2874.59 

17 

18 

2391.02 

2449.95 

2509.33 

2569.13 

2629.42 

2690.22 

2751.50 

2813.29 

2875.63 

18 

19 

2392.00 

2450.94 

2510.33 

2570.13 

2630.43 

2691.24 

2752.53 

2814.32 

2876.68 

19 

UO 

2392.98 

2451.92 

2511.32 

2571.13 

2631.44 

2692.26 

2753.55 

2815  36 

2877.72 

20 

21 

2393.96 

2452.91 

2512.32 

2572.13 

2632.45 

2693.28 

2754.58 

2816.39 

2878.76 

21 

22 

2394.94 

2453.89 

2513.31 

2573.13 

2633.46 

2694.30 

2/55.61 

2817.42 

2879.81 

22 

23 

2395.91 

2454.88 

2514.30 

2574.13 

2634.47 

2695.31  2756.63 

2818.46 

2880.85 

23 

24 

2396.89 

2455.87 

2515.30 

2575.13 

2635.48 

2696.33 

2757.66 

2819.49 

2881.89 

24 

25 

2397.87 

2456.85 

2516.29 

2576.13 

2636.  *9 

2697.55 

2758.68 

2820.52 

2882.94 

25 

26 

2398.85 

2457.84 

2517.28 

2577.13 

2637.50 

2698.37 

2759.71 

2821.56 

2883.  y  8 

26 

27 

2399.83 

2458.82 

2518.27 

2578.13 

2638.50 

2699.39 

2760.73 

2822.59 

2885.02 

27 

28 

2400.80 

2459.81 

2519.27 

2579.13 

2639.51 

2700.40 

2761.76 

2823.62 

2886.06 

28 

29 

2401.78 

2460.80 

2520.26 

2580.13 

2640.52 

2701.42 

2762.79 

2824.6o 

2887.11 

29 

1  30 

2402.76 

2461.78 

2521.25 

2581.13 

2641.53 

2702.44 

2763.81 

2825.69 

2888.15 

30 

31 

2403.74 

2462.77 

2522.25 

2582  13 

2642.54 

2703.46 

2764.84 

2826.73 

2889.20 

31 

32 

2404.72 

2463.76 

2523.24 

25N314 

2643.55 

2704.48 

2765.87 

2827.77 

2890.24 

32 

33 

2405.71 

2464.75 

2524.24 

2584.14 

2644.57 

2705.50 

2766.90 

2828.81 

2891.29 

33 

34 

2406.69 

2465.74 

2525.23 

2585.15 

2645.58 

2706.52 

2767.93 

2829.85 

2892.34 

34 

35 

2407.67 

2466.73 

2526.23 

2586.15 

2646  59 

2707.54 

2768.96 

2830.89 

2893.39 

35 

36 

2408.65 

2467.72 

2527.22 

2587,16 

2647.60 

2708.56 

2769.99 

2831.92 

2894.43 

36 

37 

2409.63 

2468.71 

2528.22 

2588.16 

2648.62 

2709.58 

2771.02 

2832.96 

2895.48 

37 

38 

2410-61 

2469.69 

2529.21 

2589.17 

2649.63 

2710.60 

2772.04 

2834.00 

2896.53 

38 

39 

2411.60 

2470.68 

2530-21 

2590.17 

2650.64 

2711.62 

2773.07 

2835.04 

2897.57 

39 

40 

2412.58 

2471.67 

2531.20 

2591.18 

2651.65 

2712.64 

2774.10 

2836.08 

2898.62 

40 

41 

1-413.56 

2472.66 

2532.20 

2592.18 

2652.67 

2713.66 

2775.13 

2837.12 

2899.  67 

41 

42 

2414.54 

2473.65 

2533.19 

2593.18 

2653.68 

2714.68 

2776.16 

2838.16 

2900.71 

42 

43 

2415.52 

2474.64 

2534.19 

2594  19 

2654.69 

2715.70 

2777.19 

2839.20 

2901.76 

43 

44 

2416.50 

2475.63 

2535.18 

2595.19 

2655.70 

2716.72 

2778.22 

2840.24 

2902.81 

44 

45 

2417.49 

2476.62 

2536.18 

2596.20 

2656.71 

2717.74 

2779.25 

2841.28 

2903.86 

45 

46 

2418.47 

2477.61 

2537.17 

2597.20 

2657.73 

2718.76 

2780.28 

2842.31 

2904.90 

•16 

1  47 

2419.45 

2478.60 

2538.17 

2598.21 

2658.74 

2719.78 

2781.31 

2843.35 

2905.95 

47 

48 

•J4-.-0.43 

2479.59 

2539.17 

2599.21 

2659.75 

2720.80 

2782.34 

2844.39 

2907.00 

48 

49 

2121.41 

2480.58 

2540.16 

2600  22 

2660.76 

2721.82 

2783.37 

2845  43 

2908  04 

49 

50 

2422.39 

2481.57 

2541.16 

2601.22 

2661.78 

2.22.84 

2784.40 

2846.47 

2909.09 

50 

51 

2423.38 

2482.56 

2542.15 

2602.23 

2662.',  9 

2723.86 

2,85.43 

2847.51 

2910.14 

5L 

52 

2424.36 

2483.54 

2543.15 

2603.23 

2,563.80 

2724.88 

2786.45 

2848  55 

2911.18 

52 

53 

2425.34 

2484.53 

2544.14 

2604.24 

2664.81 

2725.90 

2787.48 

2849  59 

2912-23 

53 

54 

2126.32 

2485.52 

2545.14 

2605.24 

2665.83 

2726.92 

2788.51 

2850.63 

2913.28 

54 

55 

2427.30 

2480.5! 

2546.13 

2606.24 

2666.*  4 

2727.94 

2789.54 

2651.67 

2914.32 

55 

56 

2428-28 

2487.£0 

2547.13 

26  17.25 

2667.85 

272896 

2790.57 

2852.70 

2915.36 

56 

57 

2429.27 

2488.49 

2548.12 

2608.25 

2668.  P6 

2729.98 

2791.60 

2853.74 

2916.41 

57 

58 

2430.25 

2489.48  2549.12 

2609.26 

2669.87  2731.00  2792.63 

2854.78 

2917.46 

5S 

59 

2431.2  J 

2490.47  ;  2550.11 

2610.26  2670.89  [  2732.02  L  2793.66  i  2855.82  2918.50 

59 

24 


RAILROAD  CURVE  TABLES. 

/ 

54° 

55° 

56°   57°   58°  |  59° 

60°  |  61°  |  62° 

0 

2919.55  2982.81 

3046.64 

3111.10  I  3176.14 

3241.86 

3308.21  3375.20 

3442.93 

0 

1 

29.:0.60 

2983.87 

3047.71 

3112.18 

3177.23 

3242.96 

3309.32 

3376.33 

3444.07 

1 

2 

2921.65 

2984.93 

3048.78 

3113.26 

3178.32 

3244.06 

3310.44 

3377.45 

3445.20 

2 

3 

2922.71 

2986.00 

3049.86 

3114.34 

3179.42 

3245.17 

3311.55 

3378.58 

3446.34 

3 

4 

2923.76 

2987.06 

3050.93 

3115.42 

3180.51 

3246.27 

3312.67 

3379.70 

3447.48 

4 

5 

2924.81 

2988.12 

3052.00 

3116.51 

3181.60 

3247.37 

3313.78 

3380.83 

3448.61 

5 

6 

2925.86 

2989.18 

3053.07 

3117.59 

3182.69 

3248.47 

3314.89 

3381.95 

3449.75 

6 

7 

2926.92 

2990.24 

3054.14 

3118.67 

3183.79 

3249.57 

3316.01 

3383.08 

3450.88 

7 

8 

21)27.97 

2991.31 

3055.  '/I 

3119.75 

3184.88 

3250.68 

3317.12 

3384.20 

3452.02 

8 

g 

2929.02 

2992.37 

3056.-29 

31-20.83 

3185.97 

3251.78 

3318.24 

3385.33 

3453.16 

9 

10 

2930.07 

2993.43 

3057.36 

3121.91 

3187.06 

3252.88 

3319.35 

3386.45 

3454.29 

10 

11 

2931.13 

2994.49 

3058.43 

3122.99 

3188.16 

3  j  53.98 

3320.46 

3387.58 

3455.43 

11 

12' 

2932.18 

2995.55 

3059.50 

3124.07 

3189.25 

3255.08 

3321.58 

3388.70 

3456.57 

12 

13 

2933.23 

2996.62 

3060.57 

31-25.15 

3190.34 

3256.19 

3322.69 

3389.83 

3457.70 

13 

14 

2934.28 

2997.68 

3061.64 

3126.23 

3191.43 

3257.29 

3323.80  !  3390.95 

3458.84 

14 

15 

2935.33 

2998.74 

3062.72 

3127.32 

3192.52 

3258.39 

33-24.92  3392.08 

3459.97 

15 

16 

2936.39 

2999.80 

3063.79 

3128.40 

3193.62 

3259.49 

3326.03  3393.20 

3461.11 

16 

17 

2937.44 

3000.86 

3064.86 

3129.48 

3194.71 

3260.59 

3327.15  3394.33 

3462.25 

17 

18 

2938.49 

3001.93 

3065.93 

3130.56 

3195.80 

3261.70 

33-28.26 

3395.45 

3463.38 

18 

19 

2939.54 

3002.99 

3067.00 

31  31.64 

3196.89 

3262.80 

3329.36 

3396.58 

3464.52 

19 

20 

2940.60 

3004.05 

3068.07 

3132.72 

3197.99 

32(13.90 

3330.49 

3397.70 

3465.66 

20 

21 

2941.65 

3005.11 

3069.15 

3133.80 

3199.08 

3265.00 

3331.60 

3398.83 

3466.79 

21 

22 

2942.70 

3006.17 

3070.22 

3134.S8 

3200.17 

3266.10 

3332.71 

3399.95 

3467.93 

22 

23 

2943.75 

3007.24 

3071.29 

3135.96 

3201.26 

3267.21 

3333.83 

3401.08 

3*69.07 

23 

24 

2944.81 

3008.30 

3072.36 

3137.04 

3202.36 

3268.31 

3334.94 

3402.20 

3470.20 

24 

25 

2945.86 

3009.36 

3073.43 

3138.13 

3203.45 

3269.41 

3336.05 

3403.33 

3471.34 

25 

26 

2946.91 

3010.4-2 

3074.50 

3139.21 

3204.54 

3270.51 

3337.17 

3404.45 

3472.47 

26 

27 

2947.96 

3011.48 

3075.58 

3140.29 

3205.63 

3271.61 

3338.28 

3405.58 

3473.61 

27 

28 

2949.01 

3012.55 

3076.65 

3141.37 

3206.73 

3272.72 

3339.40 

3406.70 

3474.75 

28 

29 

2950.07 

3013.61 

3077.72 

3142.45 

3207.82 

3273.82 

3340.51 

3407.83 

3475.88 

29 

30 

2951.12 

3014.67 

3078.79 

3143.53 

3208.91 

3274.92 

3341.62 

3408.95 

3477.02 

J30 

31 

2952.18 

3015.74 

3079.87 

3144.62 

3210.01 

3276.03 

3342.74 

3410.08 

3478.16 

31 

32 

2953.23 

3016.80 

3080.94 

3145.70 

3211.11 

3277.14 

3343.86 

3411.22 

3479.31 

32 

33 

2954.29 

3017.87 

3082.02 

3146.79 

3212.20 

3278.25 

3344.98 

3412.35 

3480.45 

33 

34 

2955.35 

3018.93 

3083.10 

3147.88 

3213.30 

3279.36 

3346.10 

3413.48 

3481.60 

34 

35 

2956.40 

3020.00 

3084.18 

3148.97 

3214.40 

3280.47 

3347.22 

3414.61 

3482.74 

35 

36 

2957.46 

3021.06 

3085.25 

3150.05 

3215.50 

3281.58 

3348.34 

3315.75 

3483.88 

36 

37 

2958.51 

3022.13 

30H6.33 

3151.14 

3216.60 

3282.69 

3349.46 

3416.88 

3485.03 

37 

38 

2959.57 

3023.20 

3087.41 

3152.23 

3217.70 

3283.80 

3350.58 

3418.01 

3486.17 

38 

39 

2960.63 

3024.26 

3088.48 

3153.31 

3218.80 

3284.91 

3351.69 

3419.14 

3487.32 

39 

40 

2961.68 

3025.33 

3089.56 

3154.40 

3219.89 

3286.02 

3352.81 

3420.28 

3488.46 

40 

41 

2962.74 

3026.39 

3090.64 

3155.49 

3220.99 

3287.13 

3353.93 

3421.41 

3489.60 

41 

42 

2963.80 

3027.46 

3091.71 

3156.57 

3222.09 

3288.24 

3355.05 

3422.54 

3490.75 

42 

43 

2964.85 

3028.52 

3092.79 

3157.66 

3223.19 

3289.35 

3356.17 

3423.68 

3491.89 

43 

44 

2965.91 

3029.59 

3093.87 

3158.75 

3224.29 

3290.46 

3357.29 

3424.81 

3493.04 

44 

45 

2966.96 

3030.66 

3094.95 

3159.84 

3225.38 

3291.57 

3358.41 

3425.94 

3494.18 

45 

46 

2968.02 

3031.72 

3096.02 

3160.92 

3226.48 

3292.68 

3359.53 

3427.07 

3495.32 

46 

47 

2969.08 

3032.79 

3097.10 

3162.01 

3227.58 

3293.78 

3360.65 

3428.21 

3496.47 

47 

48 

2970.13 

3033.85 

3098.18 

3163.10 

3228.68 

3294.89 

3361.77 

3429.34 

3497.61 

48 

49 

2971.19 

3034.92 

3099.25 

3164.18 

3229.78 

3296.00 

3362.89 

3430.47 

3498.77 

49 

50 

2972.25 

3035.98 

3100.33 

3165.27 

3230.88 

3297.11 

3364.01 

3431.60 

3499.90 

50 

51 

2973.30 

3037.05 

3101.41 

3166.36 

3231.97 

3298.22 

3365.13 

3432.74 

3501.04 

51 

52 

2974.36 

3038.11 

3102.48 

3167.44 

3233.07 

3299.33 

3366.25 

3433.87 

3502.19 

52 

53 

2975.41 

3039.18 

3103.56 

3168.53 

3234.17 

3300.44 

3367.37 

3435.00 

3503.33 

53 

54: 

2976.47 

3040.25 

3104.64 

3169.62 

3235.27 

3301.55 

3368.48 

3436.13 

3504.48 

54 

55 

2977.53 

3041.31 

3105.72 

3170.71 

3236.37 

3302.66 

3369.60 

3437.27 

3505.62 

55 

56 

2978.58 

3042.38 

3106.79 

3171.79 

3237.47 

3303.77 

3370.72 

3438.40 

3506.76 

56 

57 

2979.64 

3043.44 

3107.87 

3172.88 

3238.56 

3304.88 

3371.84 

3439.53 

3507.91 

67 

58 

2980.70 

3044.51 

3108.95 

3173.97 

3239.66 

3305.99 

3372.96 

3440.67 

3509.05 

58 

59  I  2981.75  3045.57 

3110.02 

3175.05 

3240.76 

3307.10 

3374.08 

3441.80  3510.20 

59 

25 


RAILROAD  CURVE  TABLES. 

/ 

63°  |  64° 

65° 

66°  j  67° 

68° 

69° 

70° 

71°  |  ' 

0 

3511.34 

3580.45 

3650.41 

3721.06 

3792.57 

3864.88 

3938.11 

4012.15  |  4087.15 

0 

1 

3512.49 

3581.61 

3651.59 

3722.15 

3793.77 

3866.10 

3939.34 

4013.40  !  4088.41 

1 

2 

3513.64 

3582.78 

3652.76 

3723.44 

3794.97 

3867.31 

3940.57 

4014.64 

4089.67 

2 

3 

3514.78 

3583.94 

3653,94 

3724.62 

3796.17 

3868.5.3 

3941.80 

4015.89 

409D.93 

3 

4 

3515.93 

3585.10 

3655.11 

3725.81 

3797.38 

3869.75 

3943.03 

4017  14 

4092.19 

4 

6 

3517.08 

3586.27 

3656.29 

3727.00 

3798.58 

3870.97 

3944.26 

4018.39 

4093.45 

5 

6 

3518.23 

3587.43 

3657.46 

3726.19 

3799.78 

3872.18 

394549 

4019.63 

4094.71 

6 

7 

3519.38 

3588.59 

3658.64 

3729.38 

3800.98 

3873.40 

3946.72 

4020.88 

4095.97 

7 

8 

3520.52 

35S9.75 

3659.81 

3730.56 

3802.18 

3874.62 

3947.95 

4022.13 

4097.24 

8 

«.) 

3521.67 

3590.92 

3660.99 

3731.75 

3803.38 

3.S75.83 

3949.18 

4023.37 

4098.50 

9 

10 

3522.82 

3592.08 

3662.16 

3732.94 

3804.58 

3877.05 

3950.41 

4024.62  i  4099.76 

10 

11 

3523.97 

3593.24 

3663.33 

3734.13 

3805.78 

3878.27 

3951.64 

4025.87  4101.02 

11 

12  3525.12 

3594.41 

3664.51 

3735.32 

3806.99 

3879.48 

3952.87 

4027.11  4102.28 

12 

13 

3526.26 

3595.57 

3665  68 

3736.50 

3808.19 

3880.70 

3954.10 

4028.36  4103.54 

13 

U 

3527.41 

3596.73 

3666.86 

3737.69 

3809.39 

3881.92 

3955.33 

4029.61 

4104.80 

14 

15 

3528.56 

3597.90 

3668.03 

3738.88 

3810.59 

3883.14 

3956.56 

4i  30.86 

4106.06 

15 

16 

3529.71 

3599.06 

3669.21 

3740.07 

3811.79 

3884.35 

3957.79 

4032.10 

4107.32 

16 

17 

3530.86 

3600.22 

3670.38 

3741.26 

3812.99 

3885.57 

3959.02 

4033.35 

4108.58 

17 

18 

3532.00 

3001.38 

3671.56 

3742.44 

3814.19 

3S86.79 

3960.25 

4031.60 

41  09.84 

18 

19 

3533.15 

360255 

3672.73 

3743.63 

:-*815.39 

3888.00 

3961.48 

4035.84 

4111.10 

19 

•20 

3534.30 

3603.71 

3673.90 

3744.82 

3816.60 

3889.21 

3962.71 

4037.09 

4112.36 

20 

21 

3535.45 

3604.87 

3675.08 

3746.01 

3817.80 

3890.43 

3963.94 

4038.34 

4113.62 

21 

22 

3536.60 

3606.04 

3676.25 

3747.20 

3819.00 

3891.64 

3965.17 

4039.58 

4114.89 

22 

•23 

3537.74 

3607.20 

3677.43 

3748.38 

3820.20 

3892.86 

3966.40 

4040.83 

4116.15 

23 

•21 

3538.89 

3608.36 

3678.60 

3749.57 

3821.40 

3894.08 

3967.63 

4042.08 

4117.41 

24 

25 

3540.04 

3609.53 

3679.78 

3750.76 

3822.C.O 

3895.29 

3968.86 

4043.33 

4118.67 

25 

26 

3541.19 

3610.69 

3680.95 

3751.95 

3823.80 

3896.51 

3970.09 

4044.57 

4119.93 

26 

27 

3542.34 

3611.85 

3682.13 

3753.14 

3825.01 

3897.73 

3971-32 

4045.82 

4121.19 

27 

28 

3543.48 

3613.01 

3683.30 

3754.32 

3826.21 

3898.95 

3972.55 

4047.07 

4122.45 

28 

•2'.) 

3544.63 

3614.18 

3684.48 

3755.51 

3827.41 

3900.16 

3973.78 

4048.31 

4123.71 

29 

30 

3545.78 

3615.34 

3685.65 

3756.70 

3828.61 

3901.38 

3975.01 

4049.56 

4124.97 

30 

31 

3546.94 

3616.51 

3686.83 

3757.90 

3829.82 

3902.60 

3976.25 

4050.81 

4126.24 

31 

32 

3548.09 

3617.68 

3688.01 

3759.09 

3831.03 

3903.83 

3977.49 

4052.07 

4127.51 

32 

33 

3549.25 

3618.85 

3689.19 

3760.29 

3832.24 

3905.05 

3978.72 

4053.32 

4128.78 

33 

34 

3550.40 

3620.02 

3690.37 

3761.48 

3833.45 

3906.28 

3979.96 

4054.57 

4130.05 

34 

35 

3551.56 

3621.19 

3691.55 

3762.68 

3834.66 

31107.50 

3981.20 

4055-83 

4131.32 

35 

36 

3552.72 

3622.35 

3692.73 

3763.87 

3835.86 

3908.73 

3982.44 

4057.08 

4132.59 

36 

37 

3553.87 

3623.52 

3693.91 

3765.07 

3837.07 

3909.95 

3983.68 

4058.33 

4133.86 

37 

38 

3555.  C  3 

3624.69 

3695.09 

3766.27 

3838.28 

3911.17 

3984.91 

4059.58 

4135.13 

38 

39 

3556.18 

3625.86 

3696.27 

3767.46 

3839.49 

3912.40 

398(5.15 

4060.84 

4136.40 

39 

40 

3557.34 

3627.03 

3697.45 

3768.66 

3840.70 

3913.62 

3987.39 

4062.09 

4137.67 

40 

41 

3558.49 

3628.20 

3698.63 

3769.85 

3841.91 

3914.85 

3988.63 

4063.34 

4138.94 

41 

42 

3559.65 

3629.37 

3699.81 

3771.05 

3843.12 

3916.07 

3989.87 

4064.60 

4140.21 

42 

13 

3560.80 

3630.54 

3  00.99 

3772.24 

3844.33 

3917.30 

3991.10 

4065.85 

4141.48 

43 

44 

3561.96 

3631.71 

3702.17 

3773,44 

3845.54 

3918.52 

3992.34 

4067.10 

4142.75 

44 

-:5  3563.12 

3612.88 

3703.35 

3774.64 

3846.75 

3919.74 

3993.58 

4068.36 

4144-02 

45 

46 

3564.27 

3634.04 

3704.53 

3775.83 

3847.95 

3920.97 

3994.82 

4069.61 

4145.29 

46 

!47 

3565.43 

3635.21 

3705*72 

3777.03 

3849.16 

3922.19 

3996.06 

4070.86 

4146.56 

47 

18 

3566.58 

3636.38 

3706.90 

3778.22 

3850.37 

3923.42 

3997.29 

4072.11 

4147.83 

48 

4  it 

3567.74 

3637.55 

3708.08 

3779.42 

3851.58 

3924.61 

3998.52 

4073.37 

4149  10 

49 

60 

3568.89 

3638.72 

3709.26 

3780.61 

3852.79 

3925.87 

3999.77 

4074.62 

4150.37 

50 

51 

3570.05 

3639.89 

3710.44 

3781.81 

3854.00 

3927.09 

4001.01 

4075.87 

4151.64 

51 

52 

3571.21 

3841.06 

3711.62 

3783.01 

3855.21 

3928.31 

4002.25 

4077.13 

4152.91 

52 

i53 

3572.36 

3642.23 

3712.80 

3784.20 

3856.42 

3929.54 

4003  48 

4078.38 

4154.18 

53 

54 

3573.52 

3613.40 

3713.98 

3785.40 

3857.63 

3930.76 

4004.72 

4079.63 

4155.45 

54 

55 

3574.67 

3644.57 

3715.16 

•3786.59 

3858.84 

3931.99 

4005.96 

4080.89  4156.72 

55 

56 

3575.83 

3(545.73 

3716.34 

3787.79  3860.04 

3933.21 

4007.20 

4082.14 

4157.99 

56 

57 

3576.99 

3646.90 

3717.52 

3788.98 

3861.25 

3934.44 

4008.44 

4083.39  41  59.26 

57 

58 

3578.14 

36S8.07 

3718.70 

3790.18 

3862.46 

3935.66 

4009.67 

4084.64  416053 

58 

59 

3579.30 

3649.24 

3719.88 

3791.38 

3863.67 

3936.88 

4010.91 

4085.90  ,  4161.80 

59 

26 


RAILROAD  CURVE  TABLES. 

' 

72°  |  73° 

74° 

75° 

76°  j  77° 

78° 

79° 

80°  j  ' 

0 

4163.07 

4239.97 

4317.84 

4396.74 

4476.73 

4557.81 

4640.04 

4723.41 

4808.04 

0 

1 

4164.35 

4241.26 

4319.15 

4398.07 

4478.08 

4559.18 

4641.43 

4724.82 

4809.47 

1 

2 

4165.63 

4242.56 

4320.46 

4399.40 

4479.42 

4560.54 

4642.81 

4726.22 

4810.89 

2 

3 

4166.90 

4243.85 

4:321.77 

4400.73 

4480.77 

4561.91 

4614.20 

4727.63 

4812.32 

3 

4 

4168.18 

4245.14 

4323.08 

4402.06 

4482.12 

4563.27 

4645.58 

4729.03 

4813.74 

4 

5 

4169.46 

4246.44 

4324.39 

4403.39 

4483.46 

4564.64 

4646.97 

4730.44 

4815.17 

5 

6 

4170.74 

4247.73 

4325.70 

4404.71 

4484.81 

4566.01 

4648.35 

4731.85 

4816.59 

6 

7 

4172.02 

4249.02 

4327.01 

4406.04 

4486.16 

4567.37 

4649.74 

4733.25 

4818.02 

7 

8 

4173.29 

4250.31 

4328.32 

4407.37 

4487.51 

4568.74 

4651.12 

4734.66 

4819.44 

8 

9 

4174.57 

4251.61 

4329.63 

4408.70 

4488.85 

4570.10 

4652.50 

4736.06 

4820.87 

9 

10 

4175.85 

4252.90 

4330.94 

4410.03 

4490.20 

4571.47 

4653.89 

4737.47 

4822.29 

10 

11 

4177.13 

4254.19 

4332.25 

4411.36 

4491.55 

4572.83 

4655.27 

4738.87 

4823.72 

11 

12 

4178.41 

4255.49 

4333.56 

4412.69 

4492.89 

4574.20 

4656.66 

4740.28 

4825.14 

12 

13 

4179.68 

4256.78 

4334.87 

4414.02 

4494.24 

4575.56 

4658.04 

4741.68 

4826.57 

13 

14 

4180.96 

4258.07 

4336.18 

4415.35 

4495.59 

4576.93 

4659.43 

4743.09 

4827.99 

14 

15 

4182.24 

4259.36 

4337.49 

4416.68 

4496.93 

4578.30 

4660.81 

4744.50 

4829.42 

15 

16 

4183.52 

4260.66 

4338.80 

4418.01 

4498.28 

4579.66 

4662.20 

4745.90 

4830.84 

16 

17 

4184.80 

4261.95' 

4340.11 

4419.34 

4499.63 

4581.03 

4663.58 

4747.31 

4832.27 

17 

18 

4186.07 

4263.24 

4341.42 

4420.67 

4500.98 

4582.39 

4664.97 

4748.71 

4833.69 

18 

19 

4187.35 

4264.54 

4342.73 

4422.00 

4502.32 

4583.76 

4666.35 

4750.12 

4835.12 

19 

20 

4188.63 

4265.83 

4344.05 

4423.33 

4503.67 

4585.12 

4667.73 

4751.52 

4836.54 

20 

'A 

4189.91 

4267.12 

4345.36 

4424.65 

4505.01 

4586.49 

4669.12 

4752.93 

4837.97 

21 

22 

4191.19 

4268.42 

4346.67 

4425.98 

4506.35 

4587.86 

4670.50 

4754.34 

4839.39 

22 

23 

4192.46 

4269.71 

4347.98 

4427.31 

4507.70 

4589.22 

4671.89 

4755.74 

4840.82 

23 

'24 

4193.74 

4271.00 

4349.29 

4428.64 

4509.05 

4590.59 

4673.27 

4757.15 

4842.24 

24 

25 

4195.02 

4272.29 

4350.60 

4429.97 

4510.39 

4591.95 

4674.66 

4758.55 

4843.67 

25 

26 

4196.30 

4273.59 

4351.91 

4431.30 

4511.74 

4593.32 

4676.04 

4759.96 

4845.09 

26 

'27 

4197.57 

4274.88 

4353.22 

4432.63 

4513.09 

4594.69 

4677.43 

4761.37 

4846.52 

27 

28 

4198.85 

4276.17 

4354.53 

4433.96 

4514.44 

4596.05 

4678.81 

4762.77 

4847.94 

28 

29 

4200.13 

4277.47 

4355.84 

4435.29 

4515.78 

4597.42 

4680.20 

4764.18 

4849.37 

29 

30 

4201.41 

4278.76 

4357.15 

4436.62 

4517.13 

4598.78 

4681.58 

4765.58 

4850.79 

30 

31 

4202.70 

4280.06 

4358.47 

4437.96 

4518.49 

4600.15 

4682.97 

4766.99 

4852.23 

31 

32 

4203.98 

4281.36 

4359.79 

4439.29 

4519.84 

4601.53 

4684.37 

4768.41 

4853.66 

32 

33 

4205.27 

4282.67 

4361.11 

4440.63 

4521.20 

4602.91 

4685.76 

4769.83 

4855.10 

33 

34 

4206.55 

4283.97 

4362.43 

4441.97 

4522.55 

4604.28 

4687.16 

4771.24 

4856.53 

34 

35 

4207.84 

4285.27 

4363.75 

4443.30 

4523.91 

4605.66 

4688.55 

4772.66 

4857.97 

35 

36 

4209.12 

4286.58 

4365.07 

4444.64 

4525.27 

4607.03 

4689.94 

4774.07 

4859.41 

36 

37 

4210.41 

4287.88 

4366.39 

4445.98 

4526.62 

4608.41 

4691.34 

4775.49 

4860.84 

37 

38 

4211.69 

4289.18 

4367.71 

4447.32 

4527.98 

4609.78 

4692.73 

4776.90 

4862.28 

38 

39 

4212.98 

4290.48 

4369.03 

44*8.65 

4529.33 

4611.16 

4694.13 

4778.32 

4863.71 

39 

40 

4214.26 

4291.79 

4370.35 

4449.99 

4530.69 

4612.53 

4695.52 

4779.73 

4865.15 

40 

41 

4215.55 

4293.09 

4371.67 

4451.33 

4532.05 

4613.91 

4696.92 

4781.15 

4866.59 

41 

42 

4216.83 

4294.39 

4372.99 

4452.66 

4533.40 

4615.28 

4698.31 

4782.56 

4868.03 

42 

43 

4218.12 

4295.69 

4374.31 

4454.00 

4534.76 

4616.66 

4699.70 

4783.98 

4869.46 

43 

44 

4219.40 

4297.00 

4375.63 

4455.34 

4536.11 

4618.03 

4701.10 

4785.39 

4870.90 

44 

45 

4220.69 

4298.30 

4376.94 

4456.67 

4537.47 

4619.41 

4702.49 

4786.81 

4872.33 

45 

46 

4221.98 

4299.60 

4378.26 

4458.01 

4538.83 

4620.78 

4703.89 

4788.22 

4873.77 

46 

47 

4223.26 

4300.91 

4379.58 

4459.35 

4540.18 

4622.16 

4705.28 

4789.64 

4875.21 

47 

48 

4224.55 

4302.21 

4380.90 

4460.69 

4541.54 

4623.53 

4706.67 

4791.05 

4876.61 

48 

49 

4225.83 

4303.51 

4382.22 

4462.02 

4542.89 

4624.91 

4708.07 

4792.47 

4878.08 

49 

50 

4227.12 

4304.81 

4383.54 

4463.36 

4544.25 

4626.29 

4709.47 

4793.89 

4879.52 

50 

51 

4228.40 

4306.12 

4384.86 

4464.70 

4545.61 

4627.66 

4710  86 

4795.30 

4880.95 

51 

52 

4229.69 

4307.42 

4386.18 

4466.03 

4546.96 

4629.04 

4712-25 

47%.  72 

4882.39 

52 

53 

4230.97 

4308.72 

4387.50 

4467.37 

4548.32 

4630.41 

4713.G5 

4798.13 

4883.83 

53 

54 

4232.26 

4310.02 

4388.82 

4468.71 

4549.67 

4631.79 

4715.04 

4799.55 

4885.26 

54 

55 

4233.54 

4311.33 

4390.14 

4470.04 

4551.03 

4633.16 

4716.44 

4800.96 

4886.70 

55 

56 

4234.83 

4312.63 

4391.46 

4471.38 

4552.39 

4634.54 

4717.83 

4802.38 

4888.13 

56 

57 

4236.11 

4313.93 

4392.78 

4472.72 

4553.74 

4635.91 

4719.22 

4803.79 

4889.57 

57 

58 

4237.40 

4315.23 

4394.10 

4474.06 

4555.10 

4637.29 

4720.62 

4805.21 

4891.00 

68 

59 

4238.68  1  4316.54 

4395.42 

4475.39 

4556.45 

4638.66 

4722.01 

4806.62 

4892-44 

59 

RAILROAD  CURVE  TABLES. 

'  !  81° 

82°   83° 

84° 

85°  |  86° 

87° 

88°  |  89°  |  ' 

0 

4893  88 

4980.97 

5069.44 

5159.29 

5250.57 

5343.28 

5437.54 

5533.35 

5630.81 

0 

i 

4895.33 

4982.44 

5070.93 

5160.80 

5252.11 

5344.84 

5439.13 

5534.97 

5632.46 

1 

2 

4896.77 

4983  91 

5072.42 

5162.32 

5253.65 

5346.41 

5440.72 

5536  59 

5634.10 

2 

3 

4898.22 

4985.38 

5073.92 

5163.83 

5255.19 

5347.97 

5442.31 

5538.20 

5635.75 

3 

4 

4899.66 

4986.85 

507541 

5165.35 

5256.73 

5349.54 

5443.90 

5539.82 

5637.39 

4 

5 

4901.11 

4988.32 

5076.90 

5166.86 

5258.27 

5351  10 

5445.50 

5541.44 

5639.04 

5 

6 

4902.56 

4989.78 

5078.39 

5168.38 

5259.81 

5352  67 

5447.09 

5543.06 

5640.69 

6 

7 

4904.00 

4991.25 

5079.88 

5169.89 

5261.35 

5354.23 

544868 

5544.68 

5642.33 

7 

8 

4905.45 

4992.72 

5081  38 

5171.41 

5262.88 

5355.79 

5450.27 

5546  29 

5643.98 

8 

9 

4906.89 

4994.19 

5082.87 

5172.92 

5264.42 

5357.36 

5451.86 

5547.91 

564563 

9 

10 

4908.34 

4995.66 

5084.36 

5174.44 

5265.96 

5358.92 

5453.45 

5549.53 

5647.27 

10 

11 

4909.78 

4997.13 

5085.85 

5175.95 

5267.50 

5360.49 

5455.04 

5551.14 

5648.92 

11 

12 

4911.23 

4998.60 

5087.34 

5177.47 

5269.04 

5362  05 

5456.63 

5552.76 

5650.57 

12 

13 

4912.68 

5000.07 

5088.84 

5178.98 

5270.58 

5363.62 

5458.22 

5554.38 

5652.21 

13 

14 

4914.12 

5001.54 

5090.33 

5180.50 

5272.12 

5365.18 

5459.81 

5556.00 

5653.86 

14 

15 

4915.57 

5003.01 

5091.82 

5182.01 

5273.66 

5366.74 

5461.41 

5557.62 

5655.50 

15 

16 

4917.01 

5004.47 

5093.31 

5183.53 

5275.20 

5368.31 

5463.00 

5559.24 

5657.15 

16 

17 

4918.46 

5005.94 

5094.80 

5185.04 

5276.74 

5369.87 

5464.59 

5560.85 

5658.80 

17 

18 

4919.91 

5007.41 

5096.30 

5186.56 

5278.28 

5371.44 

5466.18 

5562  47 

5660.44 

18 

19 

4921.35 

5008.88 

5097.79 

5188.07 

5279.82 

5373.00 

5467.77 

5564.09 

5662.09 

19 

20 

4922-79 

5010.35 

5099.28 

5189.58 

5281.36 

5374.57 

5469.36 

5565.70 

5663-74 

20 

21 

4924.24 

5011.82 

5100.77 

5191.10 

5282.90 

5376.13 

5470.95 

5567.32 

5665.38 

21 

22 

4925.69 

5013.29 

5102.26 

5192.61 

5284.44 

5377.69 

5472.54 

5568.94 

5667.03 

22 

23 

4927.13 

5014.76 

5103.76 

5194.13 

5285.97 

5379.26 

5474.13 

5570.56 

5668.67 

23 

24 

4928.58 

5016.23 

5105.25 

5195.64 

5287.51 

5380.82 

5475.72 

5572.18 

5670.32 

24 

25 

4930.02 

5017.69 

5106.74 

5197.16 

5289.05 

5382.39 

5477.32 

5573.79 

5671.97 

25 

26 

4931.47 

5019-16 

5108.23. 

5198.67 

5290.59 

5383.95 

5478.91 

5575.41 

5673.61 

26 

27 

4932.92 

5020.63 

5109.72 

5200.19 

5292.13 

5385.51 

5480.50 

5577.03 

5675.26 

27 

28 

4934.36 

5022.10 

5111.22 

5201.70 

5293.67 

5387.08 

5482.09 

5578.65 

5676.91 

28 

29 

4935.81 

5023.57 

5112.71 

5203.22 

5295.21 

5388.64 

5483.68 

5580.27 

5678.55 

29 

30 

4937.25 

5025.04 

5114.20 

5204.73 

5296.75 

5390.21 

5485.27 

5581.88 

5680.20 

30 

31 

4938  71 

5026  52 

5115.70 

5206.26 

5298.30 

5391.79 

5486.87 

5583.51 

5681.86 

31 

32 

4940.16 

5028  00 

5117.21 

5207.79 

5299.85 

5393.37 

5488.48 

5585.14 

5683.52 

32 

33 

4941.62 

5029.48 

5118.71 

5209.31 

5301.40 

5394.94 

5490.08 

5586.77 

5685.18 

33 

34 

4943.08 

5030.96 

5120.21 

5210.84 

5302.95 

5396.52 

5491  68 

5588.40 

5686.84 

34 

35 

4944  54 

5032  44 

5121.72 

5212.37 

5304.51 

5398.10 

5493.29 

5590.04 

5688.50 

35 

36 

4945.99 

5033.92 

5123.22 

5213.90 

5306.06 

5399.68 

5494.89 

5591.67 

5690.16 

36 

37 

4947.45 

5035.40 

5124.72 

5215.43 

5307.61 

5401.25 

5496.49 

5593.30 

5691.82 

37 

38 

4948.91 

5036.88 

5126.22 

5216  95 

5309.16 

5402.83 

5498.09 

5594.93 

5693.48 

38 

39 

4950.36 

5038  36 

5127.73 

5218.48 

5310,71 

5404.41 

5499.70 

5596.56 

5695.14 

39 

40 

4951.82 

5039.84 

5129.23 

5220.01 

5312.26 

5405.99 

5501.30 

5598.19 

5696.80 

40 

41 

4953.28 

5041.32 

5130.73 

5221.54 

5313.81 

5407.56 

5502.90 

5599.82 

5698.46 

41 

42 

4954.74 

5042.80 

5132.24 

5223  07 

5315.36 

5409.14 

5504.50 

5601.45 

5700.12 

42 

43 

4956.19 

5044.28 

5133.74 

5224.59 

5316.91 

5410.72 

5506.11 

5603.08 

5701.78 

43 

44 

4957.65 

5045.76 

5135.24 

5226.12 

5318.46 

5412.30 

5507.71 

5604.71 

5703.44 

44 

45 

4959.11 

5047.24 

5136.75 

5227.65 

5320.02 

5413.88 

5509.31 

5606.35 

5705.10 

45 

46 

4960.57 

5048.72 

5138.25 

5229.18 

5321  57 

5415.45 

5510.91 

5607.98 

5706.76 

46 

47 

4962.02 

5050  20 

5139.75 

5230.71 

5323.12 

5417.03 

5512.52 

5609.61 

5708.42 

47 

48 

4963.48 

5051.68 

5141.25 

5232.23 

5324.67 

5418.61 

5514.12 

5611.24 

5710.08 

48 

49 

4964.94 

5053.16 

5142.76 

5233.76 

5326.22 

5420.19 

5515.72 

5612.87 

5711.74 

49 

50 

4966.40 

5054.64 

5144  26 

5235.29 

5327.77 

5421.76 

551732 

5614.50 

5713.40 

50 

51 

4967.85 

5056.12 

5145.76 

5236.82 

5329.32 

5423  34 

5518.93 

5616.13 

5715.06 

51 

52 

4979.31 

5057.60 

5147.27 

5238.35 

5330.87 

5424.92 

5520.53 

5617.76 

5716.72 

52 

53 

4970.77 

5059.08 

5148.77 

5239.87 

5332.42 

5426.50 

5522.13 

5619.39 

5718  38 

53 

54 

4972.22 

5060.56 

5150.27 

5241.40  i  5333.97 

5428.07 

5523.74 

5621.02 

5720.04 

54 

55 

4973.68 

5062.04 

5151.77 

5242.93  5335.53 

5429.65 

5525.34 

5622.66 

5721.70 

55 

56 

4975.14 

5063.52 

5153.28 

5244.46  5337.08 

5431.23 

5526.94 

5624.29 

5723.36 

56 

57 

4976.60  5065.00 

5154.78 

5245.99 

5338.63 

5432.81 

5528.54 

5625.92 

5725.02 

57 

58 

4978.05 

5066.48 

5156.28 

5247.51 

5340.18 

5434.39 

5530.15 

5627.55 

5726.68 

58 

59 

4979.51 

5067-96 

5157.79 

5249.04 

5341.73 

5435.96 

5531.75 

5629.18 

5728.34 

59 

28 


TABLE  or  MINUTES  WITH  COK- 

KESPONDING  DECIMALS. 

TABLE  OF  SECONDS  WITH  COKEES- 
PONDING  DECIMALS. 

M.  |   D.   |  M.  |   D.    S.     D.   |  S.     D. 

/ 
1 

o 

0.0166 

i 
31 

o 

0.5167 

1 

it 
0.0002778 

n 
31 

0 

0.0086111 

2 

0.0333 

32 

0.5333 

2 

0.0005556 

32 

0.0088888 

3 

0.0500 

33 

0.5500 

3 

0.0008333 

33 

9.0091666 

4 

0.0667 

34 

0.5667 

"^4 

0.0011111 

34 

0.0094444 

5 

0.0833 

35 

0.5833 

5 

0.0013888 

35 

0.0097222 

6 

0.1000 

36 

0.6000 

6 

0.0016666 

36 

0.0100000 

7 

0.1167 

37 

0.6167 

7 

0.0019444 

37 

0.0102777 

8 

0.1333 

38 

0.6333 

8 

0.0022222 

38 

0.0105555 

9 

0.1500 

39 

0.6500 

9 

0.0025000 

39 

0.0108333 

10 

0.1667 

40 

0.6667 

10 

0.0027777 

40 

0.0111111 

11 

0.1833 

41 

0.6833 

11 

0.0030555 

41 

0.0113888 

12 

0.2000 

42 

0.7000 

12 

0.0033333 

42 

0.0116666 

13 

0.2167   43 

0.7167* 

13 

0.0036111 

43 

0.0119444 

14 

0.2333   44 

0.7333 

14 

0.0038888 

44 

0.0122222 

15 

0.2500 

45 

0.7500 

15 

0.0041666 

45 

0.0125000 

16 

0.2667 

46 

0.7667 

16 

0.0044444 

46 

0.0127777 

17 

0.2833 

47 

0.7833 

17 

0.0047722 

47 

0.0130555 

18 

0.3000 

48 

0.8000 

18 

0.0050000 

48 

0.0133333 

19 

0.3167 

49 

0.8167 

19 

0.0052777 

49 

0.0136111 

20 

0.3333 

50 

0.8333 

'  20 

0.0055555 

50 

0.0138888 

21 

0.3500 

51 

0.8500 

21 

0.0058333 

51 

0.0141666 

22 

0.3667 

52 

0.8667 

22 

0.0061111 

52 

0.0144444 

23 

0.3833 

53 

0.8833 

23 

0.0063888 

53 

0.0147222 

24 

0.4000 

54 

0.9000 

24 

0.0066666 

54 

0.0150000 

25 

0.4167 

55 

0.9167 

25 

0.0069444 

55 

0.0152777 

26 

0.4333 

56 

0.9333 

26 

0.0072222 

56 

0.0155555 

27 

0.4500 

57 

0.9500 

27 

0.0075000 

57 

0.0158333 

28 

0.4667 

58 

0.9667 

28 

0.0077777 

58 

0.0161111 

29 

0.4833 

59 

0.9833 

29 

0.0080555 

59 

0.0163888 

30 

0.5000 

60 

1.0000 

30 

0.0083333 

60 

0.0166666 

RAILROAD    CURVE   TABLE. 


The  following  Table  shows  the  distance  from  the  point  of  inter- 
section of  the  Tangent  lines  to  the  beginning  of  one  degree  curves, 
for  each  30  feet,  the  angle  of  deflection  (  =  angle  at  centre)  being 
known. 

I.  =  The  given  angle  of  deflection. 
II.  =  The  sought  for  distance. 
III.  =  Difference  for  intermediate  angles. 


30 


RAILROAD    CURVE    TABLE. 

I 

II 

III     |          I 

II 

III 

i    !  ii 

III 

0°    0' 

25.00 

25.0 

30°  30' 

1562.17 

26.8 

60°  30' 

3341.62 

33.4 

1 

50.02 

25.0 

31 

1589.04 

26.9 

61 

3375.20 

33.6 

1    30 

75.01 

25.0 

31     30 

1616.03 

27.0 

61    30 

3408.95 

33.8 

2 

9999 

25.0 

32 

1643.08 

27.0 

62 

3142.93 

34.0 

2     30 

125.03 

25.0 

32     30 

1670.12 

27.0 

62    30 

3477.02 

34.1 

3 

150.07 

25.0 

33 

1697.28 

27.2 

63 

3511.34 

343 

3    30 

175.05 

25.0 

33    30 

1724.56 

27.3 

63     30 

3545.78 

34.4 

4 

200.09 

25.0 

34 

1751.83 

27.3 

64 

3580.45 

3i.7 

4     30 

225.13 

25.0 

34    30 

1779.22 

27.4 

64    30 

3615.34 

31.9 

5 

250.17 

25.0 

35 

1808.67 

27.4 

65 

3650.41 

351 

5    30 

275.21 

25.0 

35     30 

1834.17 

27.5 

65     30 

3685  65 

35.2 

6 

300.30 

25.0 

36 

1861.79 

27.6 

66 

3721.06 

35.4 

6    30 

325.35 

25.0 

36    30 

1889.47 

27.7 

66     30 

3756.70 

356 

7 

350.44 

25.1 

37 

1917.26 

27.8 

67 

3792.57 

359' 

7    30 

375.54 

25.1 

37     30 

1945.05 

27.8 

67     30 

3828.61 

36.0 

8 

400.70 

25.1 

38 

1973.01 

27.9 

68 

3864.88 

36.3 

8    30 

425.79 

25.1 

38    30 

2001.03 

28.0 

68    30 

3901.38 

36.5 

9 

450.95 

25.1 

39 

2029.11 

28.1 

69 

3938.11 

36.7 

9    30 

476.10 

25.1 

39     30 

2057.30 

28.2 

69    30 

3975.01 

36.9 

10 

501.32 

25.2 

40 

2085.55 

28.3 

70 

4012.15 

37.1 

10    30 

526.53 

25.2 

40     30 

2113.91 

2-1.4 

70     30 

4019.56 

37.4 

11 

551.74 

25.2 

41 

2142.33 

28.4 

71 

4087.15 

37.6 

11     30 

576.95 

25.2 

41     30 

2170.92 

28.6 

71     30 

4124.97 

37.8 

12 

602.22 

25.3 

42 

2199.52 

28.6 

72 

4163.07 

3-1.1 

12    30 

627.55 

25.3 

42    30 

2228.28 

28.8 

72    30 

4201.41 

38.3 

13 

652.87 

25.3 

43 

2257.10 

28.8 

73 

4239.97 

38.6 

13    30 

678.20 

25.3 

43    30 

2286.04 

28.9 

73     30 

4278  76 

38.8 

14 

703.53 

25.3 

44 

2315.09 

29.0 

74 

4317.84 

38.9 

It    30 

728.97 

25.4 

44    30 

2344.20 

29.1 

74    30 

4357.15 

39  3 

15 

754.35 

25.4 

45 

2373.42 

29.2 

75 

4396.74 

39.6 

15     30 

779.79 

25.4 

45    30 

2402.76 

29.3 

75    30 

4436.62 

*  39.9 

16 

805.29 

25.5 

46 

2432.21 

29.4 

76 

4476.73 

40.1 

1C    30 

830.79 

25.5 

46    30 

2161.78 

29.6 

76    30 

4517.13 

40.4 

17 

856.35 

25.5 

47 

2491  46 

29.7 

77 

4557.81 

40.7 

17    30 

881.90 

25.5 

47    30 

2521.26 

29.8 

77    30 

4598.78 

41,0 

18 

907.52 

25.6 

48 

2551.11 

29.8 

78 

4640.04 

41.3 

18    30 

933.18 

25.6 

48    30 

2581.13 

30.0 

78    30 

4681.58 

415 

19 

958.86 

25.7 

49 

2611.27 

30.1 

79 

4723.41 

41.8 

19    30 

984.58 

25.7 

49    30 

2641.53 

30.3 

79    30 

4765.58 

42.2 

10 

1010.37 

25.8 

50 

2671.90 

30.4 

80 

4808.04 

42.5 

20    30 

1036.15 

25.8 

50    30 

2702.44 

30.5 

80    30 

4850.79 

42.7 

21 

1062.00 

25.8 

51 

2733.04 

30.6 

81 

4893.88 

43.1 

2t     30 

1089.90 

25.9 

51     30 

2763.81 

30.8 

81    30 

4937.25 

43.3 

22 

1113.80 

25.9 

52 

2791.69 

30.9 

82 

4980.97 

43.7 

22    30 

1139.75 

25.9 

52    30 

2825.68 

31.0 

82    30 

5025.04 

44,1 

23 

1165.76 

26.0 

53 

2856.86 

31.2 

83 

5069.44 

44.4 

23    30 

1191.84 

26.1 

53    30 

2888.15 

31.3 

83    30 

5114.20 

44.8 

24 

1217.9f5 

26.1 

54 

2919.55 

31.4 

84 

5159.29 

45.1 

24    30 

1244.10 

26.1 

54    30 

2951.12 

31.6 

84    30 

5204.73 

45.4 

25 

1270.28 

26.2 

55 

2982.81 

31.7 

85 

5250.57 

45.8 

25    30 

1296.58 

26.3 

55    30 

3014.67 

31.9 

85    30 

5296.75 

46.2 

26 

1322.88 

26.3 

56 

3046.64 

32.0 

86 

5343.28 

46.5 

26    30 

1349.24 

26.4 

56    30 

3078.79 

32.2 

86    30 

5390.21 

46.9 

27 

1375.65 

26.4 

57 

3111.10 

32.3 

87 

5437.54 

47.3 

27    30 

1402.10 

26.4 

57    30 

3143.53 

32.4 

87    30 

5485.27 

47.7 

28 

1428.65 

26.5 

58 

3176.14 

32.6 

88 

5533.35 

48.1 

28    30 

1455.25 

26.6 

58    30 

3208.91 

32.8 

88    30 

5581.88 

48.5 

29 

1481.89 

26.6 

59 

3241.86 

32.9 

89 

5630.81 

•  48.9 

29     30 

1508.59 

26.7 

59     30 

3274.92 

33.1 

89    30 

5680.20 

49.4 

30 

1535.30 

26.7 

60 

3308.21 

33.3 

90 

5730.00 

49.8 

31 
RAILROAD    CURVES. 


THE    FOLLOWING    TABLE    SHOWS    THE    METHOD    OF 

KEEPINGS     THE     FIELD     NOTES 

OF  A  SURVEY,  FROM  WHICH   THE  CENTER  LINE   IS  LAID  ON  THE  MAP 


From 

sta- 
tion. 

TO 
sta- 
tion. 

Length 
of  tan- 
gents in 
feet. 

Length  of 
curves  in 
feet 

Angle  at  in- 
tersection 
of    tangents 
or  angle  at 
centre. 

Course  of 
tangent, 
and 
degree 
and  direc- 
tion of 
curves. 

Radius 
of 
curves 
in  feet. 

No.  of 
ft.  from 
intersec- 
tion of 
tangents 
tobegng. 
of  curve. 

Tangent 

S  19°  21'  E 

0. 

2. 

200. 

7°        24' 

3°  42'  L 

1548.65 

100.14 

2. 

26. 

2400. 

24°        00' 

1°  00'  R 

5730. 

1217.98 

26. 

43.556 

1755.60 

Tangent 

S     2°  45'  E 

43.556 

61.681 

1812.5 

36°        15' 

2°  00'  R 

2865. 

937.82 

61.681 

93.650 

3196.90 

Tangent 

S  33°  30'  W 

93.650 

102.517 

886.7 

13°        18' 

1°  30'  L 

3820. 

445.37 

102  517 

143.90 

4138.30 

Tangent 

S  20°  12'W 

143.90 

155.766 

1186.66 

23°        44' 

2°  00'  L 

2865. 

602.02 

155.766 

170.43 

1466.40 

Tangent 

S     3°  32'  E 

170.43 

181.296 

•1086.66 

21°        44' 

2°  00'  11 

2865. 

550.00 

181.296 

184.506 

321.00 

Tangent 

S  18°  12'  W 

184.506 

193.195 

868.89 

13°        02' 

1°  30'  R 

3820. 

436-37 

193.195 

213.064 

1986.9 

Tangent 

S  31°  14'  W 

213.064 

220.908 

784.44 

11°       46' 

1°  30'  L 

3820. 

393.61 

220.908 

230.546 

963-8 

Tangent 

S  19°  28'  \V 

230.546 

242.496 

1195.00 

23°        54' 

2°  00'  R 

2865. 

606.37 

242.496 

252.356 

98600 

Tangent 

S  43°  22'  W 

252.356 

263.756 

1140.00 

17°        06' 

1°  30'  L 

3820. 

574.30 

263.756 

266.02 

226.40 

Tangent 

S  26°  16'  W 

266.02 

268.02 

200.00 

3° 

1°  30'  L 

3820. 

100.05 

268.02 

277.21 

918.89 

27°        34' 

3°         L 

1910. 

468.55 

277.21 

279.21 

200.00 

3°        00' 

1°  30'  L 

3820. 

100.05 

279.21 

289.011 

980.1 

Tangent 

S     7°  18'  E 

289.011 

291.011 

200.00 

3°       00' 

1°  30'  R 

3820. 

100.05 

291.011 

301.422 

1041.10 

31°        14' 

3°  00'  R 

1910. 

53'..88 

301.422 

303.00 

157.80 

2°        22' 

1°  30'  R 

3820. 

78.90 

303.00 

321.00 

1800. 

Tangent 

S   29°  18'  W 

321.00 

334.00 

1300. 

26° 

2°          L 

2865. 

661.44 

334. 

338.71 

471.00 

Tangent 

S    3°  18'  W 

338.71 

347.15 

844.16 

16°       53' 

2°  00'  R 

2865. 

425.19 

347.15 

364.00 

1685.00 

Tangent 

S  20D  11'  W 

364. 

376.633 

1263.33 

37°       54' 

3°           it 

1910. 

655.80 

376.633 

389.53 

389.70 

Tangent 

S  58  3  05'  W 

380.53 

392.38 

1185. 

23°        42' 

2°          R 

2865. 

601.14 

392.38 

402-92 

1054.00 

Tangent 

S  81=  47'  W 

402.92 

404.92 

200. 

3°         00' 

1°  30'  L 

3820. 

100.05 

404.92 

418.198 

1327.77 

39°        50' 

3=  00'  L 

1910. 

632.04 

418.198 

420.198 

200. 

Tangent 

S  383  57'  W 

420.198 

441.002 

2080.41 

83°        13' 

4°          L 

1432. 

1272.21 

441.002 

442.582 

158. 

4°         00' 

2°  32'  L 

22G1.87 

79.99 

442.582 

449. 

641.8 

Tangent 

S  48D  16'  E 

22.262.90 

22.637.31 

32  EXCAVATION    AND    EMBANKMENT. 

APPLICATION    OF    THE    PEISMOIDAL    FOBMULA 

IN  DETEKMINING    THE    QUANTITIES    OF    RAILKOADS    AND    CANAL    EXCAVA- 
TIONS AND  EMBANKMENTS. 


In  order  to  obtain  the  mean  area  from  transverse  sections,  con- 
struct from  the  average  cuttings  and  average  horizontal  distances 
of  the  slopes  of  the  end  section,  a  middle  section ;  and  add  to  four 
times  the  area  of  this  section  the  area  of  the  end  sections,  and  take 
one-sixth  of  the  product  for  the  mean  area. 

The  following  diagrams  show  most  of  the  figures  which  occur  in 
taking  cross  sections  of  railroads,  and  serve  to  illustrate  the  ap- 
plication of  the  formula.  In  practice,  however,  intermediate  sec- 
tions would  be  taken  between  station  0  and  station  1,  and  at  such 
other  joints  as  any  sudden  or  material  change  in  the  surface 
would  seem  to  require. 

The  cuttings- and  horizontal  distances  from  the  centre  to  the  ter- 
mination of  the  slopes,  are  set  down  in  tabular  form.  The  notes  of 
the  middle  section  may  at  convenience  be  interlined  in  the  space 
between  the  notes  of  the  end  sections.  From  this  form  the  factors 
for  the  areas  are  made  without  resorting  to  diagrams. — Page  34. 

*It  will  be  seen  by  inspecting  the  diagrams  that  the  embankment 
between  stations  3  and  4  assumes  the  shape  of  a  pyramid,  and  hence 
one-third  of  the  area  of  the  embankment  set  opposite  station  4, 
should  be  multiplied  by  the  distance  between  stations  3  and  4  to 
obtain  the  quantity.  Between  stations  4  and  5  the  excavation  as- 
sumes the  same  form,  and  should  also  be  calculated  as  a  pyramid ; 
or  construct  the  middle  section  as  before  described,  and  calculate 
the  distance  from  the  centre  to  the  point  where  the  surface  and  the 
grade  intersect ;  and  make  out  the  factors  accordingly. 

Having  obtained  the  mean  areas,  proceed  as  hereinafter  des- 
cribed to  ascertain  the  cubic  yards, 


EXCAVATION    AND    EMBANKMENT. 


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EXCAVATION    AND    EMBANKMENT. 


35 


JMV113AJN  tt.iYl.ttJN  T. 

STATION  0.               AKEAS. 

On             n      nnn 

STATION  4.               AREAS. 

MIDDLE  SECTION. 

16.      X     5.  =  80. 
20.      X     6.  =120. 
25.      X     8.  =200. 

19. 

X     5.  =  95.^-2.=  47.5. 

MIDDLE  SECTION. 

400.-r-2.=200. 

STATION    1. 

22.      X  10.  =220. 

19. 
15. 

X     5.5=104.5 
X     1.  =  15. 

119.5-^-2.=  59.75. 

zU.        X    15s.  —  z4U. 
40.      X  16.  =640. 

STATION    5. 

1100.-h2.=550. 

MIDDLE  SECTION. 

19.75  X     8.  =158. 
9.50  X  20.  =190. 
32.50  X   12.  =390. 

19. 
20. 

X     6.  =114. 
X     2.  =  40. 

154.  -^2.=  77. 

738.-^-2.=369. 

STATION    2. 

17.50  X     6.  =105. 
20.      X     7.  =140. 
25.      X     8.  =200. 

20.5 
20. 
16. 

MIDDLE  SECTION. 

X     7.  =143.5 
X     5.  =100. 
X     4.  =  64. 

445.-r-2.=222.5. 

MIDDLE    SECTION. 

13.75  X     3.  =  41.25 
20.      X     4.5=  90. 
22.      X     6.  =132. 

22. 

20 

307.5-r-2.=153.75. 

STATION  6. 

X     8.  =176. 

X      8    —  1fiO 

263.25.  ~2.=131.62. 

22. 

X     8.  =176. 

20.      X     2.  =  40. 
19.      X     4.  =  76. 

512.-r-2.=256. 

116.  -=-2.=  58. 

MIDDLE  SECTION. 

12.8    X     1.  =  12.80 
18.25  X     3.5=  63.88 

16. 
20. 
16. 

MIDDLE  SECTION. 
X      4.   =  64. 

X     4.  =  80. 
X     4.  =  64. 

76.68.  -4-2.=  38.34. 

STATION    4. 

17.5    x     3.  =  52.5  -f-2.=  26.25. 

STATION    5. 

—  •  —  _  n 

0. 

208.  -f-  2=104. 

STATION    7. 
0                ft 

EXCAVATION  AND  EMBANKMENT. 


The  cubic  yards  between  station  0  and  station  1  according  to 
the  method  of  adding  the  end  areas  and  taking  one-half  for  the 
mean  area  =  1018.51  c.  yds.  {  c.  yds. 

By  2d  (or  Prismoidal  method)=  833.33       "        f  185.18 


2d 

1st 
2d 

1st 
2d 

1st 
2d 
Error  on  500   lineal 


There  are  other  methods  which  approximate  nearer  than  the 
averaging  method.  For  instance,  taking  |iths  of  the  difference 
between  the  end  areas,  (or  tne  difference  0X0.46)  and  adding  it  to 
the  lesser  end  area  for  the  mean. 

This  method  approximates  nearer  the  true  quantity.  The  prin- 
cipal discrepancy  occurs  where  the  embankment  assumes  the 
wedge  or  pryamidal  form. — 


,atioi 

1  1  and  2  = 
land  2 

1430.55 
1387.96 

1 

42.59 

2  and  3 
2  and  3 

519.44 
498.14 

[ 

21.30 

3  and  4 
3  and  4 

156.01 
146.66 

'•      1 

9.35 

4  and  5 

48.59 

<       ( 

4  and  5 

32.40          '       1 

16.19 

feet 

of   excavation    -       -          =274.61 

By  3d 
"2d 

method  between  station  0  and  1 
"       (or  Prismoidal)  0  and  1 

937.03 
833.33 

i 

cubic  yards. 
4-    103.70 

"3d 
"2d 

"       between  station  1  and  2 
1  and  2 

1382.03 
1387.96 

\ 

— 

5.93 

"3d 
"2d 

« 

2  and  3 
2  and  3 

495.08 
498.14 

\ 

— 

3.06 

"3d 
"2d 

u 

i 

'        3  and  4 
3  and  4 

151.31 
146.66 

i 

— 

4.65 

"3d 
"2d 

r> 

«' 

4  and  5 
4  and  5 

44.72 
32.40 

i 

•f 

12.32 

Error  on  500  lineal  feet  of  excavation 

102.38 

Another  method  is  to  multiply  £  of  the  distance  between  trans- 
verse sections,  by  the  sum  of  the  end  areas,  added  to  four  times 
half  their  sum ;  and  dividing  by  27  for  the  cubic  yards. 

The  results  are  the  same  as  by  the  first  method  except  between 
stations  0  and  1. 


EXCAVATION  AND  EMBANKMENT.  3v 


EXPLANATION  OF  THE  FOLLOWING  TABLES. 

The  tables  are  calculated  for  a  distance  of  100  feet  between  trans- 
verse sections. 

In  the  left  hand  column  are  given  the  areas  in  feet.  To  obtain  the 
cubic  yards  for  areas,  without  decimals,  look  in  the  second 
column  under  the  head  of  0,  and  opposite  the  given  area,  find  the 
cubic  yards. 

EXAMPLE. — Kequired  the  number  of  cubic  yards  for  an  area  of 
190  feet.  In  the  second  column,  under  the  head  of  0,  and  opposite 
190  in  the  first  column,  find  703.70  cubic  yards. 

To  obtain  the  cubic  yards  for  a  less  distance  than  100  feet,  multi- 
ply the  cubic  yards  found  in  the  tables  bv  the  given  distance,  and 
point  off  the  fractional  parts  of  100  feet. 

If  the  area  has  decimal  parts,  pass  the  eye  to  the  right,  opposite 
the  area  of  the  whole  number,  and  under  the  head  of  such  decimal 
will  be  found  the  number  of  yards. 

EXAMPLE.— Eequired  the  cubic  yards  for  an  area  of  105.4  feet.  In 
the  sixth  column,  under  the  head  of  40,  and  opposite  105  in  the  first 
column,  are  given  390.37  cubic  yards. 

If  the  yards  for  an  area  greater  than  354.90,  and  not  exceeding 
3549  feet,  are  required,  the  decimal  point  of  the  area  given  in  the 
tables,  and  that  of  the  cubic  yards,  being  removed  one  figure  to  the 
right,  will  give  the  required  yards.  If  there  are  decimal  parts,  add 
the  cubic  yards  found  opposite  0  in  the  first  column,  under  the 
head  of  such  decimal. 

EXAMPLE.— Eequired  the  cubic  yards  for  an  area  of  1975  feet ;  re- 
move the  decimal  point  one  figure  to  the  left,  and  find  the  yards  for 
an  area  of  197.5  feet  =  731.48,  then  remove  the  decimal  point  one 
figure  to  the  right  and  you  have  7314.8  cubic  yards.  If  there  is  a 
decimal,  add  the  cubic  yards  found  for  such  decimal. 

Or,  to  obtain  the  cubic  yards  for  an  area  exceeding  3549  feet,  take 
one  half  of  the  area,  and  seek  the  corresponding  yards  in  tables 
and  multiply  the  same  by  2. 


38 


EXCAVATION    AND    EMBANKMENT    TABLES. 

|  0.00  |  0.10  |  0.20 

0.30  |0.40 

0.50  |  0.60 

0.70 

0.80  |0.90 

0 

0.00 

0.37 

0.74 

1.11 

1.48 

1.85 

2.22 

2.59 

2.96 

3.33 

1 

3.70 

4.07 

4.45 

4.81 

5.19 

5.56 

5.93 

6.30 

6.67 

7.04 

2 

7.41 

7.78 

8.15 

8.52 

8.89 

9.26 

9.63 

10.00 

10.37 

10.74 

3 

11.11 

11.48 

11-85 

12.22 

12.59 

12.96 

13.33 

13.70 

14.07 

14.44 

4 

14.82 

15.19 

15.56 

15.93 

16.30 

16.67 

17.04 

17.41 

17.78 

18.15 

5 

18.52 

18.89 

19.26 

19.63 

20.00 

20.37 

20.74 

21.11 

21.48 

21.85 

6 

22.22 

22.59 

22.96 

23.33 

23.70 

24.07 

24.44 

24.82 

25.19 

25.56 

7 

25.93 

26.30 

26.67 

27.04 

27.41 

27.78 

28.15 

28.52 

28.89 

29.26 

8 

29.63 

30.00 

30.37 

30.74 

31.11 

31.48 

31.85 

32.22 

32.59 

32.96 

9 

33.33 

33.70 

34.07 

34.44 

34.82 

35.19 

35.56 

35.93 

36.30 

36.67 

10 

37.04 

37.41 

37.78 

38.15 

38.52 

38.89 

39.26 

39.63 

40.00 

40.37 

11 

4074 

41.11 

41.48 

41.85 

42.22 

42.59 

42.96 

43.33 

43.70 

44.07 

12 

44.44 

44.82 

45.19 

45.56 

45.93 

46.30 

46.67 

47.04 

47.41 

47.78 

13 

48.15 

48.52 

48.89 

49.26 

49.63 

50.00 

50.37 

50.74 

51.11 

51.48 

14 

51.85 

52.22 

52.59 

52.96 

5^.33 

53.70 

54.07 

54.44 

54.82 

55.19 

15 

55.56 

55.93 

56.30 

56.67 

57.04 

57.41 

57.78 

58.15 

58.52 

58.89 

16 

59.26 

59.63 

60.00 

60.37 

60.74 

61.11 

61.48 

61.85 

62.22 

62.59 

17 

62.96 

63.33 

63.70 

64.07 

64.44 

64.82 

65.19 

65.56 

65.93 

66.30 

18 

66.67 

67.04 

67.41 

67.78 

68.15 

68.52 

68.89 

69.26 

69.63 

70.00 

19 

70.37 

70.74 

71.11 

71.48 

71.85 

72.22 

72.59 

72.96 

73.33 

7370 

20 

74.07 

74.44 

74.82 

75.19 

75.56 

75.93 

76.30 

76.67 

77.04 

77.41 

21 

77.78 

78.15 

78.52 

78.89 

79.26 

79.63 

80.00 

80.37 

80.74 

81.11 

22 

81.48 

81.85 

82.22 

82.59 

82.96 

83.33 

83.70 

84.07 

84.44 

84.82 

23 

85.19 

85.56 

85.93 

86.30 

86.67 

87.04 

87.41 

87.78 

88.15 

88.52 

24 

88.89 

89.26 

8963 

90.00 

90.37 

90.74 

91.11 

91.48 

91.85 

92.22 

25 

92.59 

92.96 

93.33 

93-70 

94.07 

94.44 

94.82 

95.19 

95.56 

95.93 

26 

96.30 

96.67 

97.04 

97-41 

97.78 

98.15 

98.52 

98.89 

99.26 

9963 

27 

100.00 

100.37 

100.74 

101-11 

101.48 

101.85 

102.22 

102.59 

102.96 

103.33 

28 

103.70 

104.07 

104.44 

104-82 

105.19 

105.56 

105.93 

106.30 

106-67 

107.04 

29 

107.41 

107.78 

108.15 

108-52 

108.89 

109.26 

109.63 

110.00 

110-37 

110.74 

30 

111.11 

111.48 

111.85 

112-22 

112.59 

112.96 

113.33 

113.70 

114-07 

114.44 

31 

114.81 

115.18 

11556 

115-92 

116.29 

116.67 

117.03 

117.40 

117.77 

118.15 

32 

118.52 

118.89 

119.26 

119-63 

120.00 

120.37 

120.74 

121.11 

121-48 

121.85 

33 

122.22 

122.59 

122.96 

123-33 

123.70 

124.07 

124.44 

124.81 

125.18 

125.55 

34 

125.92 

126.30 

126.66 

127-03 

127.40 

127.77 

128.14 

12851 

128.88 

129.26 

35 

129.63 

130.00 

13037 

130-74 

131-11 

131.48 

131.85 

132.22 

132-59 

132.96 

36 

133.33 

133.70 

134.07 

134-44 

134.81 

135.18 

135.55 

135.92 

136-29 

136.67 

37 

137.04 

137.41 

137.78 

138-15 

338.52 

138.89 

139.26 

139.63 

140-00 

140.37 

38 

140.74 

141.11 

141.48 

141-85 

142.22 

142.59 

142.96 

143.33 

143-70 

144.07 

39 

144.44 

144.81 

145.18 

145-55 

145.92 

146.29 

146.66 

147.03 

147-40 

147.78 

40 

148.15 

148.52 

148.89 

149-26 

149.63 

150.00 

150.37 

150.74 

151.11 

151.48 

41 

151.85 

152.22 

152.59 

152-96 

153.33 

153.70 

154.07 

154.44 

154-81 

155.18 

42 

155.55 

155.92 

156.29 

156-66 

157.03 

157.40 

157.77 

158.14 

158-51 

158.89 

43 

159.26 

159.63 

160.00 

160-37 

160.74 

161.11 

161.48 

161.85 

162-22 

162.59 

44 

162.96 

163.33 

163.70 

164-07 

164.44 

164.81 

165.18 

165.55 

165-92 

166.30 

45 

166.67 

16704 

167.41 

167-78 

168.15 

168.52 

168.89 

169.26 

169.63 

170.00 

46 

170.37 

170.74 

171.11 

171-48 

171.85 

17-2.22 

172.59 

172.96 

173.33 

173.70 

47 

174.07 

174.44 

174.81 

175-18 

175.55 

175.92 

176.29 

176.66 

177.03 

177.41 

48 

177.78 

178.15 

178.52 

178-89 

179.26 

179.63 

180.00 

180.  87 

180.74 

181.11 

49 

181.48 

181.85 

182.22 

182-59 

182.96 

183.33 

183.70 

184.07 

184.44 

184.81 

50 

185.18 

185.55 

18592 

186-29 

186.66 

187.03 

187.40 

187.77 

188.14 

188.52 

51 

188.89 

189.26 

189.63 

190-00 

190.37 

190.74 

191.11 

191.48 

191.85 

192.22 

52 

192.59 

192.96 

193.33 

193-70 

194.07 

194.44 

194.81 

195.18 

195.55 

195.93 

53 

196.30 

196.67 

197.04 

197-41 

197-78 

198.15 

198.52 

19889 

199.26 

19963 

54 

200.00 

200.37 

200.74 

201-11 

201-48 

201.85 

202.22 

202.59 

202.96 

203.33 

55 

203.70 

204.07 

204.44 

204.81 

205.18 

205.55 

205.92 

206.29 

206.66 

207.03 

56 

207.41 

207.78 

208.15 

208.52 

208.89 

209.26 

209.63 

21000 

210.37 

210.74 

57 

211.11 

211.48 

211.85 

212.22 

212.59 

212.96 

213.33 

213.70 

214.07 

214.44 

58 

214.81 

215.18 

215.55 

215.92 

216.29 

216.66 

217.03 

217.40 

217.77 

218.15 

59 

218.52 

218.89 

219.26 

219.63 

220-00 

220.37 

220.74 

221.11 

221.48 

221.85 

EXCAVATION  AND  EMBANKMENT  TABLES. 

|o.oo 

0.10 

0.20 

0.30 

0.40 

0.50  j  0.60 

0.70 

0.80 

0.90 

60 

222.22 

222.59 

222.96 

223.33 

223.70 

224.07 

224.44 

224.81 

225.18 

225.55 

61 

225.92 

226.29 

226.66 

227.03 

227.40 

227.77 

228.14 

228.51 

228.88 

229.26 

62 

229.63 

230.00 

230.37 

230.74 

231.11 

231.48 

231.85 

232.22 

232.59 

232.96 

63 

233.33 

233.70 

•234.07 

234.44 

234.81 

235.18 

235.55 

235.92 

236.29 

236.67 

64 

237.04 

237.41 

237.78 

238.15 

238.52 

238.89 

239.26 

239.63 

240.00 

240.37 

65 

240.74 

241.11 

241.48 

241.85 

242.22 

242.59 

242.96 

243.33 

243.70 

244.07 

66 

244.44 

244.81 

245.18 

245.55 

245.92 

246.30 

246.67 

247.04 

247.41 

247.78 

67 

248.15 

248.52 

248.89 

249.26 

249.63 

250.00 

250.37 

250.74 

251.11 

251.48 

68 

251.85 

252.22 

252.59 

252.96 

253.33 

253.70 

254.07 

254.44 

254.81 

255.18 

69 

255.56 

255.93 

256.30 

256.67 

257.04 

257.41 

257.78 

258.15 

258.52 

258.89 

70 

259.26 

259.63 

260.00 

260.37 

260.74 

261.11 

261.48 

261.85 

262.22 

262.59 

71 

262.96 

263.33 

263.70 

264.07 

264.44 

264.81 

265.18 

265.55 

265.92 

266.30 

72 

266.67 

267.04 

2<>7.41 

267.78 

268.15 

268.52 

268.89 

269.26 

269.63 

270.00 

73 

270.37 

270.74 

271.11 

271.48 

271.85 

272.22 

272.59 

272.96 

273.33 

273.70 

74 

274.07 

274.44 

274.81 

275.18 

275.55 

275.92 

276.29 

276.66 

277.04 

277.41 

75 

277.78 

278.15 

278.52 

278.89 

279.26 

279.63 

280.00 

280.37 

280.74 

281.11 

76 

281.48 

281.85 

282.22 

282.59 

282.96 

283.33 

283.70 

284.07 

284.44 

284.81 

77 

285.18 

285.56 

285.93 

286.30 

286.67 

287.04 

287.41 

287.78 

288.15 

288.52 

78 

288.89 

289.26 

289.63 

290.00 

290.37 

290.74 

291.11 

291.48 

291.85 

292.22 

79 

292.59 

292.96 

293.33 

293.70 

294.07 

294.44 

294.81 

295.18 

295.55 

295.93 

80 

296.30 

296.67 

297.04 

297.41 

297.78 

298.15 

298.52 

298.89 

299.26 

299.63 

81 

300.00 

300.37 

300.74 

301.11 

301.48 

301.85 

302.22 

302.59 

302.96 

303.33 

82 

303.70 

304.07 

304.44 

31*4.81 

305.18 

305.55 

305.92 

306.29 

306.66 

307.03 

83 

307.41 

307.78 

308.15 

308.52 

308.89 

309.26 

309.63 

310.00 

310.37 

310.74 

84 

311.11 

311.48 

311.85 

312.22 

312.59 

312.96 

313.33 

313.70 

314.07 

314.44 

85 

314.81 

315.19 

315.56 

315.93 

316.30 

316.67 

317.04 

317.41 

317.78 

318.15 

86 

318.52 

318.89 

319.26 

319.63 

320.00 

320.37 

320.74 

321.11 

321.48 

321.*5 

87 

322.22 

322.59 

322.96 

323.33 

323.70 

324.07 

324.44 

324.81 

325.18 

32555 

88 

325.92 

326.30 

326.67 

327.04 

327.41 

327.78 

328.15 

328.52 

328.89 

329.26 

89 

329.63 

330.00 

330.37 

330.74 

331.11 

331.48 

331.85 

332.22 

332.59 

332.96 

90 

333.33 

333.70 

334.07 

334.44 

334.81 

335.18 

335.55 

335.92 

336.29 

336.67 

91 

337.04 

337.41 

337.78 

338.15 

338.52 

338.89 

339.25 

339.62 

339.99 

340.37 

j  92 

340.74 

341.11 

341.48 

341.85 

342.22 

342.59 

342.96 

343.33 

343.70 

344.07 

93 

344.44 

344.81 

345.18 

345.56 

345.93 

346.30 

346.67 

347.03 

347.40 

347.78 

94 

348.15 

348.52 

348.89 

349.26 

349.63 

350.00 

350.37 

350.74 

351.11 

351.48 

95 

351.85 

352.22 

352.59 

352.96 

353.33 

353.70 

354.07 

354.44 

354.81 

355.18 

96 

355.55 

355.93 

356.30 

356.67 

357.04 

357.41 

357.78 

358.15 

358.52 

358.89 

97 

359.26 

359.63 

360.00 

360.37 

360.74 

361.11 

361.48 

361.85 

362.22 

362.59 

98 

362.96 

363.33 

363.70 

364.07 

364.44 

364.81 

365.18 

365.55 

365.93 

366.30 

99 

366.67 

367.04 

367.41 

367.78 

368.15 

368.52 

368.89 

369.26 

369.63 

370.00 

100 

370.37 

370.74 

371.11 

371.48 

371.85 

372.22 

372.59 

372.96 

373.33 

373.70 

101 

374.07 

374.44 

374.81 

375.18 

375.55 

375.92 

376.29 

376.67 

377.04 

377.41 

102 

377.78 

378.15 

378.52 

378.89 

379.26 

379.63 

380.00 

380.37 

380.74 

381.11 

103 

381.48 

381.85 

382.22 

382.59 

382.96 

383.33 

383.70 

384.07 

384.44 

38481 

104 

385.18 

385.55 

385.92 

386.29 

386.67 

387.04 

387.41 

387.78 

388.]  5 

388.52 

105  388.89 

389.26 

389.63 

390.00 

390.37 

390.74 

391.11 

391.48 

391.85 

392.22 

106 

392.59 

392.96 

393.33 

393.70 

394.07 

394.44 

394.81 

395.18 

395.55 

395.92 

107 

396.30 

396.67 

397.04 

397.41 

397.78 

398.15 

398.52 

398.89 

399.26 

399.63 

108 

400.00 

400.37 

400.74 

401.11 

401.48 

401.85 

402.22 

402.59 

402.96 

403.33 

109 

403.70 

404.07 

404.44 

404.81 

405.18 

405.55 

405.92 

406.29 

406.67 

407.04 

110  j  407.41 

407.78 

408.15 

408.52 

408.89 

409.26 

409.63 

410.00 

410.37 

410.74 

111  :  411.11 

411.48 

411.85 

412.22 

412.59 

412.96 

413.33 

413.70 

414.07 

414.44 

112  414.81 

415.18 

415.55 

415.92 

416.29 

416.67 

417.04 

417.41 

417.78 

418.15 

113  418.52 

418.89 

419.26 

419.63 

420.00 

420.37 

420.74 

421.11 

421.48 

421.85 

114  422.22 

422.59 

422.96 

423.33 

423.70 

424.07 

424.44 

424.81 

425.18 

425.56 

115  425.93 

426.30 

426.67 

427.04 

427.41 

427.78 

428.15 

428.52 

428.89 

429.26 

116  429.63 

430.00 

430.37 

430.74 

431.11 

431.48 

431.85 

432.22 

432.59 

432.96 

117  433.33 

433.70 

434.07 

434.44 

434.81 

435.18 

435.55 

435.92 

436.29 

436.67 

118  !  437.04 

437.41 

437.78 

438.15 

438.52 

438.89 

439.26 

439.63 

440.00 

440.37 

119  440.74 

441.11 

441.48 

441.85 

442.22 

442.59 

442.96 

443.33 

443.70 

444.07 

EXCAVATION   AND    EMBANKMENT    TABLES. 

|o.oo 

0.10 

0.20 

0.30 

0.40 

0.50 

0.60   |0.70 

0.80 

0.90 

120 

444.44 

444.81 

445.18 

445.55 

445.92 

446.29 

446.67 

44704 

447.41 

447.78 

121 

448.15 

448.52 

448.89 

449.26 

449.63 

450.00 

450.37 

450.74 

451.11 

451.48 

122 

451.85 

452.22 

452.59 

452.96 

453.33 

453.70 

454.07 

454.44 

454.81 

455.18 

123 

455.55 

455.92 

456.29 

456.67 

457.04 

457.41 

457.78 

458.15 

458.52 

458.89 

124 

459.26 

459.63 

460.00 

460.37 

460.74 

461.11 

461.48 

461.85 

462.22 

462.59 

125 

462.96 

463.33 

463.70 

464.07 

464.44 

464.81 

465.18 

465.55 

465.93 

46630 

126 

466.67 

467.04 

467.41 

467.78 

468.15 

468.52 

468.89 

469.26 

469.63 

470.00 

127 

470.37 

470.74 

471.11 

471.48 

471.85 

472.22 

472.59 

472.96 

473.33 

473.70 

128 

474.07 

474.44 

474.81 

475.18 

475.56 

475.93 

476.30 

476.67 

477.04 

477.41 

r;9 

477.78 

478.15 

478.52 

478.89 

479.26 

479.63 

480.00 

480.37 

480.74    481.11 

130 

481.48 

481.85 

482.22 

482.59 

482.96 

483.33 

483.70 

484.07 

484.44 

484.81 

131 

485.18 

485.55 

485.92 

486.29 

486.67 

487.04 

487.41 

487.78 

488.15 

488.52 

132 

488.89 

489.26 

489.63 

490.00 

490.37 

490.74 

491.11 

491.48 

491.85 

492.22 

133 

492.59 

492.96 

493.33 

493.70 

494.07 

494.44 

494.81 

495.19 

495.56 

495.93 

134 

496.30 

496.67 

497.04 

497.41 

497.78 

498.15 

498.52 

498.89 

499.26 

499.63 

135 

500.00 

500.37 

500.74 

501.11 

501.48 

501.85 

502.22 

502.59 

502.96 

503.33 

136 

503.70 

504.07 

504.44 

504.81 

505.18 

505.56 

505.93 

506.30 

506.67 

507.04 

137 

507.41 

507.78 

508.15 

508.52 

508.89 

509.26 

509.63 

510.00 

510.37 

510.74 

138 

511.11 

511.48 

511.85 

512.22 

512.59 

512.96 

513.33 

513.70 

514.07 

514.44 

139 

514.81 

515.18 

515.55 

515.92 

516.29 

516.67 

517.04 

517.41 

517.78 

518.15 

140 

518.52 

518.89 

519.26 

519.63 

520.00 

520.37 

520.74 

521.11 

521.48 

521.85 

141 

522.22 

522.59 

522.96 

523.33 

523.70 

524.07 

524.44 

524.81 

525.19 

525.56 

142 

525.93 

526.30 

526.67 

527.04 

527.41 

527.78 

528.15 

528.52 

528.89 

529.26 

143 

529.63 

530.00 

530.37 

530.74 

531.11 

531.48 

531.85 

532.22 

532.59 

532.94 

144 

533.33 

533.70 

534.07 

534.44 

534.81 

535.18 

535.56 

535.93 

536-30 

536.67 

145 

537.04 

537-41 

537.78 

538.15 

538.52 

538.89 

539.26 

539.63 

540.00 

540.37 

146 

540.74 

541.11 

541.48 

541.85 

542.22 

542.59 

542.96 

543.33 

543.70 

544.07 

147 

544.44 

544.81 

545.18 

545.56 

545.93 

546.30 

546.67 

547.04 

547.41 

547.78 

148 

548.15 

548.52 

548.89 

549.26 

549.63 

550.00 

550.37 

550.74 

551.11 

551.48 

149 

551.85 

552.22 

552.59 

552.96 

553.33 

553.70 

554.07 

554.44 

554.81 

555.18 

150 

555.55 

555.93 

556.30 

556.67 

557.04 

557.41 

557.78 

558.15 

558.52 

558.89 

151 

559.26 

559.63 

560.00 

560.37 

560.74 

561.11 

561.48 

561.85 

562.22 

562.59 

152 

562.96 

563.33 

563.70 

564.07 

564.44 

564.81 

565.18 

565.56 

565.93 

566.30 

153 

566.67 

567.04 

567.41 

567.78 

568.15 

568.52 

568.89 

569.26 

569.63 

570.00 

154 

570.37 

570.74 

571.11 

571.48 

671.85 

572.22 

572.59 

572-96 

573.33 

573.70 

155 

574.07 

574.44 

574.81 

575.18 

575.56 

575.93 

576.30 

576.67 

577.04 

577.41 

156 

577.78 

678.15 

578.52 

578.89 

579.26 

579.63 

580.00 

580.37 

580.74 

581.11 

157 

581.48 

581.85 

582.22 

582.59 

582.96 

583.33 

583.70 

584.07 

584.44 

584.81 

158 

585.18 

585.55 

585.92 

586.29 

586.66 

587.04 

5x7.41 

587.78 

588.15 

588.52 

159 

588.89 

589.26 

589.63 

590.00 

590.37 

590.74 

591.11 

591.48 

591.85 

59222 

160 

592.59 

592.96 

593.33 

593.70 

594.07 

594.44 

594.81 

595.18 

595.55 

595.92 

161 

596.29 

596.67 

597.04 

597.41 

597.78 

598.15 

598.52 

598.89 

599.26 

599.63 

162 

600.00 

600.37 

600.74 

601.11 

601.48 

601.85 

602.22 

602.59 

602.96 

603.33 

163 

603.70 

604.07 

604.44 

604.81 

605.18 

605.55 

605.92 

606.30 

606.67 

607.04 

164 

607.41 

607.78 

608.15 

608.52 

608.89 

609.26 

609.63 

610.00 

610.37 

610.74 

165 

611.11 

611.48 

611.85 

612.22 

612.59 

612.96 

613.33 

613.70 

614.07 

614.44 

166 

614.81 

615.18 

615.55 

615.92 

616.29 

616.67 

617.04 

617.41 

617.78 

618.15 

167 

618.52 

618.89 

619.26 

619.63 

620.00 

620.37 

620.74 

621.11 

621.48 

621.85 

168 

622.22 

622.59 

622.96 

623.33 

623.70 

624.07 

624.44 

624.81 

625.18 

625.56 

169 

625.93 

626.30 

626.67 

627.04 

627.41 

627.78 

628.15 

628.52 

628.89 

629.26 

170 

629-63 

630.00 

630.37 

630.74 

631.11 

631.48 

631.85 

63222 

632.59 

632.96 

171 

633.33 

633.70 

634.07 

634.44 

634.81 

635.18 

635.55 

635.92 

636.29 

636.66 

172 

637.04 

637.40 

637.77 

638-14 

638.51 

638.88 

639.25 

639.62 

639.99 

640.37 

173 

640.74 

641.11 

641.48 

641.85 

642.22 

642.59 

642.96 

643.33 

643.70 

644.07 

174 

644.44 

644.81 

645.18 

645.55 

645.92 

646.29 

646.66 

647.03 

647.41 

647.78 

175 

648.15 

648.52 

648.89 

64926 

649.63 

650.00 

650.37 

650.74 

651.11 

651.48 

176 

651.85 

652.22 

652.59 

652.9(5 

653.33 

653.70 

654.07 

654.44 

654.81 

655.18 

177 

655.56 

655.93 

656.30 

656.67 

657.04 

657.41 

657.78 

658.15 

658.52 

658.89 

178 

659.26 

659.63 

660.00 

660.37 

660.74 

661.11 

661.48 

661.85 

662.22 

662.59 

179 

662.96 

663.33 

663.70 

664.07 

664.44 

664.81 

665.18 

665.55 

665.92 

666.29 

41 


EXCAVATION  AND  EMBANKMENT  TABLES. 

0.00 

0.10 

0.20 

0.30 

0.40 

0.50  |  0.60 

0.70 

0.80 

0.90 

180 

606.67 

667.04  667.41 

667.78 

668.15 

668.52 

668.89 

669.26 

669.63   670.00 

181 

670.37 

670.74 

671.11 

671.48 

671.85 

672.22 

672.59 

672.96 

673.33 

673.70 

182 

674.07 

674.44 

674.81 

675.18 

675.55 

675.93 

67630 

676.67 

677.04 

677.41 

183 

677.78 

678.15 

678.52 

678.89 

(579.26 

679.63 

680.00 

680.37 

680.74 

681.11 

184 

681.48 

681.85 

682.22 

682.59 

682.96 

683.33 

684.70 

684.07 

684.44 

684.81 

185 

685.18 

685.56 

685.93 

686  30 

686.67 

687.04 

687.41 

687.78 

688.15 

688.52 

186 

688.89 

689.26 

689.63 

690.00 

690.37 

690.74 

691.11 

691.48 

691.85 

692.22 

187 

692.59 

692.96 

693.33 

693  70 

694.07 

694.44 

694.81 

695.18 

695.55 

695.92 

188 

696.30 

696.67 

697.04 

697.41 

697.78 

698.15 

698.52 

698.89 

699.26 

699.63  ' 

189 

700.00 

700.37 

700.74 

701.11 

701.48 

701.85 

702.22 

702.59 

702.96 

703.33 

190 

703.70 

704.07 

704.44 

704.81 

705.18 

705.55 

705.92 

706.29 

706.6H 

707.03 

191 

707.40 

707.77 

708.14 

708.51 

708.89 

709.26 

70963 

710.00 

710.37 

710.74 

192 

711.11 

711.48 

711.85 

712  22 

712.59 

712.96 

713.33 

713.70 

714.07 

714.44 

193 

714.81 

715.18 

715.55 

715.92 

716.29 

716.67 

717.04 

717.41 

717.7S 

718.15 

194 

718.52 

718.89 

719.26 

719.63 

720.00 

720.37 

720.74 

721.11 

721.48 

721.85 

195 

722.22 

722.59 

722.96 

723.33 

723.70 

724.07 

724.44 

7-24.81 

725.18 

725.55 

196 

725.92 

726.29 

726.66 

727.03 

727.40 

727.77 

728.14 

728.51 

728.88 

729.25 

197 

729.63 

730.00 

730.37 

730.74 

731.11 

731.48 

731.85 

732.22 

732.59 

732.96 

198 

733.33 

733.70 

734.07 

734.44 

734.81 

735.18 

735.55 

735.93 

736.30 

736.67 

199 

737.04 

737.41 

737.78 

738.15 

738.52 

738.89 

739/26 

739.63 

740.00 

740.37 

200 

740.74 

741.11 

741.48 

741.85 

742.22 

742.59 

742.96 

743.33 

743.70 

744.07 

201 

744.44 

744.81 

745.18 

74555 

745.93 

746.30 

746.67 

747.04 

747.41 

747.78 

202 

748.15 

748.52 

748.89 

749..  6 

T49.63 

750.00 

75037 

750.74 

751.11 

751.48 

203 

751.85 

752.22 

752.59 

752.96 

753.33 

753.70 

754.07 

754.44 

754.81 

755.18 

204 

755.55 

755.93 

756.30 

756.67 

757.04 

757.41 

757.78 

758.15 

758.52 

758.89 

205 

759.26 

759.63 

760.00 

760.37 

760.74 

761.11 

761.48 

761.85 

762.22 

762.59 

206 

762.96 

763.:  !3 

763.-70 

764.  U7 

764.44 

764.81 

765.18 

765.55 

765.93 

766.30 

207 

766.66 

767.01 

767.41 

767.78 

768.15 

768.52 

76889 

769.26 

769.63 

770.00 

208 

770.37 

770.74 

771.11 

771.48 

771.85 

772.22 

772.59 

772.96 

773.33 

773.70 

209 

774.07 

774.44 

774.81 

775.18 

775.55 

775.93 

776.30 

776.  C>6 

777.04 

777.41 

210 

777.7H 

778.15 

778.52 

778.89 

779.26 

779.63 

780.00 

780.37 

780.74 

781.11 

211 

781.48 

781.85 

782.22 

78259 

78-2.96 

783.33 

783.70 

784.07 

784.44 

784.81 

212 

785.18 

785.55 

785.93 

78630 

786.66 

787.04 

787.41 

787.78 

788.15 

788.52 

213 

788.89 

789.26 

789.63 

790.00 

790.:;7 

790.74 

79111 

791.48 

791.85 

792.22 

214 

792.59 

792.96 

793.33 

793.70 

794.07 

794.44 

794.81 

795.18 

795.55 

795.93 

215 

796.30 

796.66 

797.04 

797.41 

797.78 

798.15 

798.52 

798.89 

799.'26 

799.63 

216 

sno.oo 

800.37 

800.74 

801  11 

801.48 

801.85 

80222 

802.59 

802.96 

803.33 

217 

803.70 

804.07 

804.44 

80481 

805.18 

805.55 

805.93 

806.30 

806.66 

807.04 

218 

807.41 

807.78 

808.15 

808.52 

808.89 

d09.26 

80963 

810.00 

810.37 

810.74 

219 

811.11 

811.48 

811.85 

812.22 

812.59 

812.96 

813.33 

813.70 

814.0? 

814.44 

220 

814.81 

815.18 

815.55 

815.93 

816.30 

816.66 

817.04 

817.41 

817.78 

818.15 

221 

818.52 

818.89 

819.26 

819.63 

8,0.00 

820.37 

820.74 

821.11 

821.48 

821.85 

222 

822.22 

822.59 

822.96 

823.33 

823.70 

824.07 

824.44 

824.81 

825.18 

825.55 

223 

825.93 

826.30 

826.66 

827.04 

827.41 

827.78 

828.15 

828.52 

828.89 

829.26 

224 

829.63 

830.00 

8U0.37 

830.74 

831.11 

831.48 

831.85 

832.22 

832.59 

832.96 

225 

833.33 

833.70 

834.07 

834.44 

834.81 

835.18 

83555 

835.93 

836.30 

836.66 

226 

837.04 

837.41 

837.78 

83815 

838.52 

838.89 

83926 

839.6  J 

840.00 

840.37 

|  227 

840.74 

841.11 

841.48 

841.85 

842.22 

842.59 

H42.96 

843.33 

843.70 

844.07 

I  228 

844.44 

844.81 

845.18 

845.55 

845.93 

846.30 

846  66 

847.04 

847.41 

847.78 

229 

848.15 

848.52 

848.89 

849.26 

849.63 

850.00 

850.37 

850.74 

851.11 

851.48 

230 

851.85 

852.22 

852.59 

852  96 

853.33 

853.70 

854.07 

854.44 

854.81 

855.18 

231 

855.55 

855.9} 

856.S& 

85666 

857  04 

857.41 

85778 

858.15 

858.52 

858.89 

232 

859.26 

859.63 

860.00 

86037 

860.74 

861.11 

861.48 

861.85 

862.22 

862.59 

233 

862.96 

863.33 

863.70 

864  07 

864.44 

864.81 

865.18 

8C.5.55 

865.93 

866.30 

234 

866.66 

867.04 

867.41 

867.78 

868.15 

868.52 

868.89 

869.26 

869.63 

870.00 

235 

870.37 

870.74 

871.11 

871.48 

871.85 

872.22 

872.59 

872.96 

873.33 

873.70 

236 

874.07 

874.44 

874.81 

875.18 

875.55 

875.93 

876.30 

876.66 

877.04 

877.41 

237  877.78 

878.15  |  878.52 

878.89 

879.26 

879.63 

880.00 

880.37 

880.74 

881.11 

238  881.48 

8sl.85  882.22  882.59 

882.96 

883.33 

88370 

884.07 

884.44 

884.81 

239  885.18 

885.55  885.93  '  886.30 

886.66 

887.04 

887.41 

887.78  888.15 

888.52 

42 


EXCAVATION  AND  EMBANKMENT  TABLES. 

0.00 

0.10 

0.20 

0.30   0.40  |  0.50 

0.60 

0.70  |  0.80  1  0.90 

240 

888.88 

889.26 

889.63 

890.00 

890.37 

890.74 

891.11 

891.48 

891.85 

892.22 

241 

892.59 

892.96 

893.33 

893.70 

894.07 

894.44 

894.81 

8-J5.18 

895.55 

895.93" 

242 

896.30 

896.66 

897.04 

897.41 

897.78 

898.15 

898.52 

898.88 

899.26 

899.63 

243 

900.00 

900.37 

900.74 

901.11 

901.48 

901.85 

902.22 

902.59 

902.96 

903.33 

244 

903.70 

904.07 

904.44 

904.81 

905.18 

905.55 

905.93 

906.30 

906.66 

907.04 

245 

907.41 

907.78 

908.15 

908.52 

908.88 

909.26 

909.63 

910.00 

910.37 

910.74 

246 

911.11 

911.48 

911.85 

912.22 

912.59 

912.96 

913.33 

913.70 

914.07 

914.44 

247 

914.81 

915.18 

915.55 

915.93 

•J16.30 

916.66 

917.04 

917.41 

917.78 

91815 

248 

918.52 

918.88 

919.26 

919.63 

920.00 

920.37 

920.74 

921.11 

921.48 

921.85 

249 

922.22 

922.59 

922.96 

923.33 

923.70 

924.07 

924.44 

924.81 

925.18 

925.55 

250 

925.92 

926.30 

926.66 

927.04 

927.41 

927.78 

928.15 

928.52 

928.88 

929.26 

251 

929.63 

930.00 

930.37 

930.74 

931.11 

931.48 

931.85 

932.22 

932.59 

932.96 

252 

933.33 

933.70 

934.07 

934.44 

934.81 

935.18 

935.55 

935.92 

936.30 

936.66 

253 

937.04 

937.41 

937.78 

938.15 

938.52 

938.88 

939.26 

939.63 

940.00 

940.37 

254 

940.74 

941.11 

941.48 

941.85 

942.22 

942.59 

942.96 

943.33 

943.70 

944.07 

255 

944.44 

944.81 

945.18 

945.55 

945.92 

946.30 

946.66 

947.04 

947.41 

947.78 

256 

948.15 

948.52 

948.88 

94t).26 

949.63 

950.00 

950.37 

950.74 

951.11 

951.48 

257 

951.85 

952.22 

952.59 

952.96 

953.33 

953.70 

954.07 

954.44 

954.81 

955.18 

258 

955.55 

955.92 

956.30 

956.66 

957.04 

957.41 

957.78 

958.15 

958.52 

958.88 

259 

959.26 

959.63 

960.00 

960.37 

960.74 

961.11 

961.48 

961.85 

962.22 

962.59 

260 

962.96 

963.33 

963.70 

964.07 

964.44 

964.81 

965.18 

965.55 

965.92 

266.30 

261 

966.66 

967.04 

967.41 

967.78 

968.15 

968.52 

968.88 

969.26 

969.63 

970.00 

262 

970.37 

970.74 

971.11 

971.48 

971.85 

972.22 

972.59 

972.96 

973.33 

973.70 

263 

974.07 

974.44 

974.81 

975.18 

975.55 

975.92 

976.30 

976.66 

977.04 

977.41 

264 

977.78 

978.15 

978.52 

978.88 

979.26 

979.63 

980.00 

980.37 

980.74 

981.11 

265 

981.48 

981.85 

982.22 

982.59 

982.96 

983.33 

983.70 

984.07 

984.44 

984.81 

266 

985.18 

985.55 

985.92 

986.30 

986.66 

987.04 

987.41 

987.78 

988.15 

988.52 

267 

988.88 

989.26 

989.63 

990.00 

990.37 

990.74 

991.11 

991.48 

991.85 

992.22 

268 

992.59 

992.96 

993.33 

993.70 

994.07 

994.44 

994.81 

995.18 

995.55 

995.92 

269 

996.30 

996.66 

997.04 

997.41 

997.78 

998.15 

998.52 

998.88 

999.26 

999.63 

270 

1000.00 

1000.37 

1000.74 

1001.11 

1001.48 

1001.85 

1002.22 

1002.59 

1002.96 

1003.33 

271 

1003.70 

1004.07 

1004.44 

1004.81 

1005.18- 

1005.55 

1005.92 

1006.30 

1006.66 

1007.04 

272 

1007.41 

1007.78 

1008.15 

1008.52 

1008.88 

1009.26 

1009.63 

1010.00 

1010.37 

1010.74 

273 

1011.11 

1011.48 

1011.85 

1012.22 

1012.59 

1012.96 

1013.33 

1013.70 

1014.07 

1014.44 

274 

1014.81 

1015.18 

1015.55 

1015.92 

1016.30 

1016.66 

1017.04 

1017.41 

1017.78 

1018.15 

275 

1018.52 

1018.88 

1019.26 

1019.63 

1020.00 

1020.37 

1020.74 

1021.11 

1021.48 

1021.85 

276 

1022.22 

1022.59 

1022.96 

1023.33 

1023.70 

1024.07 

1024.44 

1024.81 

1025.18 

1025.55 

277 

1025.92 

1026.30 

1026.66 

1027.04 

1027.41 

1027.78 

1028.15 

1028.52 

1028.88 

1029.26 

278 

1029.63 

1030.00 

1030.37 

1030.74 

1031.11 

1031.48 

1031.85 

1032.22 

1032.59 

1032.96 

279 

1033.33 

1033.70 

1034.07 

103i.44 

1034.81 

1035.18 

1035.55 

1035.92 

1036.30 

1036.66 

280 

1037.04 

1037.41 

1037.78 

1038.15 

1038.52 

1038.88 

1039.26 

1039.63 

1040.00 

1040.37 

281 

1040.74 

1041.11 

1041.48 

1041.85 

1042.22 

1042.59 

1012.96 

1043.33 

1043.70 

1044.07 

282 

1044.44 

1044.81 

1045.18 

1045.55 

1045.92 

1046.30 

1046.66 

1047.04 

1047.41 

1047.78 

283 

1048.15 

1048.52 

1048.88 

1049.26 

1049.63 

1050.00 

1050.37 

1050.74 

1051.11 

1051.48 

284 

1051.85 

1052.22 

1052.59 

1052.96 

1053.33 

1053.70 

1054.07 

1054.44 

1054.81 

1055.18 

285 

1055.55 

1055.92 

1056.30 

1056.66 

1057.04 

1057.41 

1057.78 

1058.15 

1058.52 

1058.88 

286 

1059.26 

1059.63 

1060.00 

1060.37 

1060.74 

1061.11 

1061.48 

1061.85 

1062.22 

1062.59 

287 

1062.96 

1063.33 

1063.70 

1064.07 

1064.44 

1064.81 

1065.18 

1065.55 

1065.92 

1066.30 

288 

1066.66 

1067.04 

1067.41 

1067.78 

1068.15 

1068.52 

1068.88 

1069.26 

1069.63 

107000 

289 

1070.37 

1070.74 

1071.11 

1071.48 

1071.85 

1072.22 

1072.59 

1072.96 

1073.33 

1073.70 

290 

1074.07 

1074.44 

1074.81 

1075.18 

1075.55 

1075.92 

1076.30 

1076.66 

1077.04 

1077.41 

291 

1077.78 

1078.15 

1078.52 

1078.88 

1079.26 

1079.63 

1080.00 

1080.37 

1080.74 

1081.11 

292 

1081.48 

1081.85 

1082.22 

1082.59 

1082.96 

1083.33 

1083.70 

1084.07 

1084.44 

1084.81 

293 

1085.18 

1085.55 

1085.92 

1086.30 

1086.66 

1087.04 

1087.41 

1087.78 

1088.15 

1088.52 

294 

1088.88 

1089.26 

1089.63 

1090.00 

1090.37 

1090.74 

1091.11 

1091.48 

1091.85 

1092.22 

295 

1092.59 

1092.96 

1093.33 

1093.70 

1094.07 

1094.44 

1094.81 

1095.18 

1095.55 

1095.92 

296 

1096.30 

1096.66 

1097.04 

1097.41 

1097.78 

1098.15 

1098.52 

1098.88 

1099.26 

1099.63 

297 

1100.00 

1100.37 

1100.74 

1101.11 

1101.48 

1101.85 

1102.22 

1102.59 

1102.96 

1103.33 

298 

1103.70 

1104.07 

1104.44 

1104.81 

1105.18 

1105.55 

1105.92 

1106.30 

1106.66 

1107.04 

299 

1107.41 

1107.78 

1108.15 

1108.52 

1108.88 

1109.26 

1109.63 

1110.00 

1110.37 

1110.74 

43 


EXCAVATION  AND  EMBANKMENT  TABLES. 

0.00 

OJO  |  0.20 

0.30 

0.40 

0.50  |  0.60 

0.70 

0.80 

0.90 

300 

1111.11 

1111.48 

1111.85  1112.22 

1112.59 

1112.96 

1113.33  [1113.70 

1114.07 

1114.44 

301 

1111.82 

1  S15.19 

1115.56  1115.93 

1116.30 

1116.67 

1117.04 

1117.41 

1117.78 

1118.15 

302 

1118.52 

1118.89 

1119.26 

1119.63 

1120.00 

1120.87 

1120-74 

1121.11 

1121.48 

1121.85 

303 

1122.22 

1122.59 

1122.96 

1123.33 

1123.70 

1124.07 

1124.44  1124.82 

1125.19 

1125.56 

304 

1125.93 

1126.30 

1126.67 

1127.04 

1127.41 

1127.78 

1128.15  1128.52 

1128.89 

1129.26 

305 

1129.63 

1130.00 

11150.37 

1130.74 

1131.11 

1131.48 

1131.85  1132.22 

1132.59 

1132.96 

306 

113:i.33 

1133.70 

1134.07 

1134.44 

1134.82 

1135.19 

1135.56  1135.93 

1136  30 

1137.617 

307 

1137.04 

1137.41 

1137.78 

1138.15 

1138.52 

1138.89 

1139.26  1139.63 

1140.00 

1140.37 

308 

1140.74 

1141.11 

1141.48 

1141.85 

1142.22 

1142.59 

1142.96 

1143.33 

1143.70 

1144.07 

309 

1144.44 

1144.82 

1145.19 

1145.56 

1145.93 

1146.30 

1146.67 

1147.04 

1147.41 

1147.78 

310 

1148.15 

11-18.52 

1148.89 

1149.^6 

1149.63 

1150.00 

1150.37  J1150.74 

115111 

1151-48 

311 

1151.85 

1152.22 

1152.59 

1152.96 

1153.33 

1153.70 

1154.07  U154.44 

1154.82 

1155.19 

312 

1155.56 

1156  93 

1156.30 

1156.67 

1157.<i4 

1157.41 

1157.78  11158.15 

1158  52 

1158.89 

313 

1159.26 

1159.63 

1160.00 

1160.37 

1160.74 

1161.11 

1161.48  (1161.85 

1162.22 

1162.59 

314 

1162.96 

1163.33 

1163.70 

1164.07 

1164.44 

1164.82 

1165.19  1165.56 

1165.93 

J166.30 

315 

1166.67 

1167.04 

1167.41 

1167.78 

1108.15 

1168.52 

1168.89  1169.26 

1169.63 

1170.00 

316 

H70.:;7 

1170.74 

1171.11 

1171.48 

1171.85 

1172.22 

1172.59  1172.96 

1173.33 

1173.70 

317 

1174.07 

1174.44 

1174.82 

1175.19 

1175.56 

1175.98 

1176.80 

1176.67 

1177.04 

1177.41 

318 

1177.78 

1178.15 

1178.52 

1178.89 

1179.26 

1179.63 

1180.00 

1180.37 

1180.74 

1181.11 

319 

1181.48 

1181.85 

1182.22 

1182.59 

1182.96 

1183.33 

1188.70  1184.07 

1184.44 

1184.82 

320 

1185.19 

1185.56 

1185.93 

1186.30 

1186.67 

1187.04 

1187.41  1187.78 

1188.15 

1188.52 

321 

1188.89 

1189.26 

1189.63 

1190.00 

1190.37  1190.74 

1191.11  ;1191.48 

119185 

1192.22 

322 

1192.59 

1192.96 

1193.33 

1193.70 

1194.07 

1194.44 

1194-82  J1195.19 

1195.56 

1195.93 

323 

1196.30 

1196.67 

1197.04 

1197.41 

1197.78 

1198.15 

1198.52  1198.89 

1199.26 

1199.63 

324 

1200.00 

1200.37 

1200.74 

1201.11 

1201.48 

1201.85 

1202.22  1202.59 

1202.96 

1203.33 

325  1203.70 

1204.07 

1204.44 

1204.82 

1205.19 

1205.56 

1205.93  1206.30 

1206.67 

1207.04 

326 

1207.41 

1207.78 

1208.16 

1208.52 

1208.89 

1209.26 

1209.63 

1210.00 

1210.37 

1210.74 

327 

1211.11 

1211.48  1211.85 

1212.22 

1212.59 

1212.96 

1213.33 

1213.70 

1214.07 

1214.44 

328 

1214.82 

1215.19 

1215.56 

1215.93 

1216.30 

1216.67 

1217.04  11217.41 

1217.78 

1218.15 

329 

1218.52 

1218.89  1219.26 

1219.63 

1220.00 

1220.37 

1220.74  (1221.  11 

1221.48 

1221.86 

330 

1222.22 

1222.59  |  1222.96 

1223.33 

1223.70 

1224.07 

1224.44  1224.81 

1225.18 

1225.55 

331 

1225.93 

1226.30 

1226.67 

1,27.04 

1227.41 

1227.78 

1228-15 

1228.52 

1228.^9 

1229.26 

332 

1229.63 

1230.00 

1230.37 

1230.74 

1231.11 

1231.48 

1231.85 

1232-22 

1232.59 

1232.96 

333 

1233.33 

1233.70 

1234.07 

1234.44 

1234.82 

1235.19 

1235.56  1235.93 

1236.30 

1236.67 

334 

1237.04 

1237.41 

1237.78 

1238.15 

1238.52 

1288.89 

1239.26 

1239.68 

1240.00 

1240.37 

335 

1240.74 

1241.11 

1241.48 

1241.85 

1242.22 

1242.59 

1242.96 

1243.33 

1243.70 

1244.07 

336 

1244.44 

1244.82 

1245.19 

1245.56 

1245.93 

1246.30 

1246.67 

1247.04 

1247.41 

1247.78 

337 

1248.15 

1248.52 

1248.89 

1249.26 

1249.63 

1250.00 

1250.37 

1250.74 

1251.11 

1251.48 

338 

1251.85 

1252.22 

1252.59 

1252.96 

1253.33 

1253.70 

1254.07 

1254.44 

1254.82 

1255.19 

339 

1255.56 

1255.93 

1256.30 

1256.67 

1257.04 

1257.41 

1257.73 

1258.15 

1258,52 

1258.89 

340 

1-59.26 

1259.63 

1260.00 

1260.37 

1260.74 

1261.11 

1261.48 

1261.85 

1262  22 

1262.59 

341 

1262.96 

1263.33 

1263.70 

1264.07 

1264.44 

1264.82 

1265.19 

1265.56 

1265.93 

1266.30 

312 

1266.67 

1267.04 

1267.41 

1267.78 

1268.15 

1268.52 

1268.89 

1269.26 

1269.63 

1270.00 

34J 

1270.37 

1270.74 

1271.11 

1271.48 

1271.85 

1272.22 

1272.59 

1272.96 

1273.33 

1273.70 

314 

1274.07 

1274.44 

1274.82 

1275.19 

1275.56 

1275.93 

1276.30 

1276.67 

1277.04 

1277.41 

315 

1277.78 

1278.15 

1278.52 

1278.89 

1279.26 

1279.63 

1280.00 

1280.37 

1280.74 

1281.11 

346 

1281.48 

1281.85 

1282.22 

1282.59 

1282.96 

1283.33 

1283.70 

1284.07 

1284.44 

1284.82 

347 

1285.19 

1285.56 

1285.93 

1286.80 

1286.67 

1287.04 

1287.41 

1287.78 

1288.15 

1288.52 

348 

1288.89 

1289.26 

1289.6$ 

1290.00 

1290.37 

1290.74 

1291.11 

1291.48 

1291.85 

1292.22 

349 

1292.59 

1292.96 

1293.33 

1293.70 

1294.07 

1294.44 

1294.82 

1295.19 

1295.56 

1295.93 

350 

1296.30 

1296.67 

1297.04 

1297.41 

1297.78 

1298.15 

1298.52 

1298  89 

1299.26 

129963 

351 

1300.00 

1300.37 

1300.74 

1301.11 

1301.48 

1301.85 

1302.22 

1302.59 

1302.96 

1303  33 

35] 

'1303.70 

1304.07 

1304.44 

1304.82 

1305.19 

1305.56 

1305.93 

1306.30 

1306  67 

1307.04 

353 

1307.41 

1307.78 

1308.15 

1308.52 

1308.89 

1309.26 

1309.63  11310.00 

1310.37 

1310.74 

'354 

1311.11 

1311.48 

1311.85 

1312.22 

1312.59 

1312.96 

1313.33  1313.70 

1314  07 

1314.44 

355 

1314.82 

1315.19 

1315.56 

1315.93 

1316.30 

1316.67 

1317.04  1317.41 

1317.78 

1318.15 

356 

1318.52 

1318.89 

1819.26 

1319.63 

1320.00 

1320.87 

1320.74  Il321.ll 

1321.48 

1321.86 

357 

1322.22 

1322.59 

1322.96 

1323-33 

1323.70 

1324.07 

1324.44  1324.81 

1325.18 

1325.55 

358 

1325.93 

1326.30 

1826.67 

1327.04 

1327.41  1327.78 

1328.15  1328.52 

1328.89  1329.26 

359 

1329.63 

1330.00  1330.87 

1330.74 

1331.11  1  1331.48 

1331.85  1332.22 

1332.59  1332.96 

44. 


INSTEUCTIONS     TO    DIVISION    AND     ASSISTANT    ENGI- 
NEERS EELATIVE  TO  FIELD  NOTES  ON  SUEVEYS 
FOE  THE  SOUTH  PENNA.  E.  E.  CO. 


First— Enter  the  names  of  the  Division  Engineer,  Senior  Assistant  Engineer 
in  charge  of  the  party,  Assistant  Engineer  at  Transit  Instrument,  Assistant 
Engineer  at  Leveling  Instrument,  Eodmen,  Chainmen,  Flagman,  Axemen, 
composing  the  partv.  Kodmen  must  make  the  same  notes,  also  enter  the 
date  and  place  where  the  work  is.. 

Second— State  in  the  column  of  remarks  on  the  first  or  second  page  of  the 
book  at  the  beginning  of  the  notes  of  any  survey  or  levels,  the  letter  of  the 
line  and  where  it  was  begun  and  where  it  is  to  be  run  to. 

Third— The  Stakes  of  all  lines  must  be  numbered  on  the  rear  face,  next  to  the 
transit,  and  must  be  lettered  on  the  forward  face,  with  the  letter  of  the  line. 
A'l  lines  must  be  lettered. 

Fourth— State  what  Datum  the  Levels  start  from  or  refer  to,  and  if  started 
from  a  Bench  state  what  Bench  and  from  what  authority  or  book  the  Elevation 
was  obtained. 

Fifth— Enter  all  notes  of  Transit  or  Level  fully  and  distinctly  in  pencil  in  the 
field— if  any  details  or  calculations  are  omitted  from  haste  or  sudden  storms 
coming  up— make  them  complete  before  the  day  is  over,  and  when  required  by 
the  Senior  Assistant  or  Division  Engineer,  they  must  be  recorded  in  a  Kecord 
Book  the  same  evening. 

Sixth— All  field  notes  must  be  compared  during  the  day  taken,  and  all 
Levelers' calculations  on  turning  points  must  be  made  by  Assistant  and  Rod- 
man, and  compared  on  fie  spot  and  found  correct  before  going  forward  witn 
the  work. 

Seventh— Benches  must  be  made  at  least  once  in  every  mile,  and  oftener  if 
opportunity  offers.  Levels  must  be  tested  on  any  existing  Benches  found 
along  the  line,  and  te.sts  made  of  the  accuracy  of  the  old  and  new  works. 
Benches  must  not  be  cut  on  shade  or  fruit  trees  and  no  unnecessary  damage 
done  in  clearing  the  line  of  sight;  offsets  must  be  made  to  save  valuable  trees 

Eighth— In  passing  through  inclosed  land  the  Senior  Assistant  will  see  thao 
the  fences  taken  down  by  the  party  are  put  up  after  they  pass  forward. 

Ninth— The  Assistant  at  the  Transit  must  record  the  names  of  land  owners, 
the  points  where  boundaries  are  crossed,  and  tbeir  courses  when  obtainable. 

Tenth— Chiefs  of  Party  must  arrange  to  get  the  party  out  and  at  their  work  as 
early  as  possible  in  the  morning,  and  keep  them  employed  until  the  proper 
hour  in  the  evening.  All  preparations  for  the  field  work  must  be  made  by  the 
Senior  Assistant  and  Assistants  the  previous  evening,  so  that  no  delays  may 
occur  in  the  morning.  Dinner  will  be  procured  by  the  Senior  Assistant  to  be 
eaten  in  the  field  when  the  party  is  more  than  one  mile  from  boarding  places. 

Boarding  expenses  paid  by  any  members  of  the  party  will  be  reported  to  the 
Senior  Assistant  and  will  be  repaid  by  the  company  at  the  end  of  the  month. 

Eleventh— Senior  Assissants  will  see  that  the  instruments,  rods  and  chains 
are  kept  in  good  order  and  adjustment  by  the  Assistants ;  any  damage  to  in- 
struments or  rods  from  want  of  proper  care  must  be  defrayed  by  the  Assistant 
having  the  same  in  charge. 

Twelfth— Daily  notes  of  the  work  done  and  the  date  must  be  entered  in  this 
field  book  every  evening. 

Thirteenth— Assistant  Engineers  in  charge  of  the  Transit  must  plot  their 
lines,  and  Assistants  in  charge  of  the  Level  must,  with  the  aid  of  their  liodman, 
make  a  profile  every  evening,  of  the  line  leveled  over  each  day. 

Fourteenth— Division  and  Senior  Assistant  Engineers  will  make  reports  of 
instruments  and  stationary  on  hand  at  the  close  ot  each  month,  and  send  them 
in  promptly  to  the  General  Office. 

Fifteenth— Division  Engineers  must  report  any  neglect  of  these  instructions 
to  the  Chief  Assistant  Engineer. 

OLIVER  W.  BAENES,  Chief  Engineer. 


Engineering    Field    Work.* 

CHAPTER    VI. 

THE    SURVEYS. 

The  three  classes  of  surveys,  viz :  Preliminary,  Location,  and 
Construction,  form  as  good  divisions  as  can  be  suggested  for  this 
subject,  and  we  will  consider  them  in  order. 

PRELIMINARY. 

The  object  of  a  Preliminary  survey  is  to  ascertain  whether  it  be 
feasible  to  build  a  line  of  railway  between  two  points  upon  the  sur- 
face of  the  earth,  and  this  information  is  obtained  for  certain 
parties  who  wish  to  make  money  in  some  way  or  other  by  con- 
structing or  having  such  line  of  railroad  constructed.  For  this 
purpose  the  parties  employ  a  more  or  less  competent  engineer  to 
make  these  surveys,  giving  him  authority  to  employ  one  or  more 
field  parties  according  to  the  magnitude  of  the  work,  and  the 
money  they  may  think  they  can  spend  upon  it.  If  only  one  party 
is  employed  it  is  sometimes  under  the  direction  of  the  chief  en- 
gineer himself,  but  more  commonly  under  an  assistant  employed 
by  him. 

ORGANIZATION    OF    FIELD    PARTY. 

The  organization  of  this  field  party  is  usually,  as  follows  : 

1.  The  Assistant  in  charge  of  the  party. 

2.  The  Transitman,  whose  work  is  running  the  line  and  keeping 
all  notes  thereof. 

3.  The  Leveler,  whose  work  is"  taking  levels,  drawing  the  profiles 
and  making  the  estimates  therefrom. 

4.  The  Level  rodman,  assistant  to  the  Leveler. 

5.  The  head  chainman,  who  should  also  carry  the  transit  rod  and 
get  therewith  the  lines  given  by  the  transitman. 

6.  The  hind  chainman,  who  should  also  number  the  stakes  and 
keep  a  record  of  all  distances  measured. 

7.  From  one  to  five  axemen  according  to  the  amount  of  chop, 
ping  required  by  the  work. 


*  Written  by  the  late  CHAS.  A.  SMITH,  C.  E..  Professor  of  Civil  and  Mechanical 
togineering  at  Washing"  TT~-' Oi    T  ~    :~      "'  --««-•—•-- 

ING  NEWS.  Vol.  III.  1876. 


Engineering  at  Washington  University,  St.  Louis,  and  published  in  ENGINEER- 
Vol.  " 


46  ENGINEERING  FIELD  WORK. 

These  may  be  considered  about  all  the  men  needed  for  the 
professional  part  of  the  work,  and  if  the  country  is  inhabited  will 
be  all  that  will  be  employed ;  if  there  are  only  a  few  inhabitants  a 
team  and  driver  may  be  advantageous,  but  if  uninhabited  and  it 
becomes  necessary  to  take  a  camp  outfit,  at  least  two  more  men  are 
indispensable— a  teamster  and  a  cook,  the  latter  being  a  very  im- 
portant member  of  the  party. 

THE    ENGINEER-IN-CHARGE. 

The  duties  of  the  engineer-in-charge  of  the  party  are  too  many 
for  enumeration  here,  but  he  has  to  see  that  the  greatest  amount 
of  work  possible  is  done  for  the  money  expended ;  his  business  is 
to  get  information  for  the  chief  engineer  and  to  keep  his  party 
running  without  delay.  A  word  of  brotherly  advice  to  him  may  not 
come  amiss  and  is  meant  kindly  if  it  is  not  necessary. 

CARE    OF    MEN. 

In  selecting  your  party  for  a  start  use  judgement  and  your  know- 
ledge of  human  nature;  don't  get  two  men  who  have  a  feud  with 
each  other  in  the  same  party  if  it  can  be  helped.  Study  your  men 
all  the  time  and  be  frank  and  free  with  them ;  do  not  talk  much 
with  them  in  working  hours,  but  watch  all  hands  very  closely,  for 
the  first  few  days  especially.  Remember  that  your  men  are  men, 
and  treat  them  well:  show  them  that  you  know  how  the  work 
should  be  done,  but  don't  "nag"  them  all  the  time ;  if  you  have  A 
horse,  don't  keep  them  at  work  till  dark  and  then  ride  off  and 
leave  them  to  walk  three  or  four  miles  to  supper,  but  either  quit 
work  in  decent  season  or  lend  your  horse  to  some  fellow  who  is 
fagged,  and  walk  in  with  your  men.;  don't  hang  round  in  the  morn- 
ing and  let  your  men  wait  for  you,  but  pick  up  an  axe  or  rod  and 
start  first  for  the  work ;  get  into  good  training  for  walking,  and  if 
you  start  for  supper  last  passall  the  men  on  the  road  ;  don't  shirk 
work  yourself,  and  don't  let  any  body  else  shirk ;  never  ask  a  man 
to  do  any  work  you  would  not  be  williug  to  do  yourself,— we  remem- 
ber "stripping  to  the  buff "  and  wading  a  stream  four  feet  deep 
when  the  cakes  of  ice  were  coming  down,  because  we  thought  the 
men  hung  back  and  did  not  want  to  go  into  the  water ;  don't  worry 
the  transitman's  wits  out  of  his  head  by  asking  him  questions ;  find 
out  what  he  is  doing  and  recording,  but  don't  crowd  him  too  hard 
or  bluster  about  Jiiin ;  don't  swear  habitually  before  the  men  it'  you 


THE  COOK-ON  THE  LINE-THE  TKANSITMAN.  47 

can  help  it ;  you  may  want  to  swear  at  them  some  times,  and  if  not 
used  to  it  they  will  be  more  apt  to  obey;  don't  scold  a  man  when 
you  are  angry  yourself,  if  you  can  help  it,  but  wait  and  talk  to 
him  after  supper,  when  you  have  cooled  down. 

THE    COOK. 

In  selecting  a  camp  outfit  be  especially  careful  to  get  a  good 
cook,  and  we  advise  a  good  cooking  stove  of  cast  iron  with  enough 
pipe  to  draw  well, — we  remember  a  sheet  iron  stove  which  had  to 
be  taken  down  every  morning  and  the  soot  kicked  out  of  it  before 
a  fire  could  be  made  to  "draw,"  and  we  also  remember  the  satis- 
faction with  which  the  boys  kicked  the  miserable  thing  to  pieces 
after  it  had  been  "returned"  at  headquarters.  We  are  more 
particular  in  this  matter,  not  only  because  we  like  to  be  well  fed, 
but  because  men  must  be  well  fed  in  order  to  work  well — and  you 
must  remember  that  poor  food  will  make  bad  temper  and  bad 
work,  and  that  the  interests  of  your  employers  demand  that  you 
keep  your  men  contented  with  their  job.  So  much  for  the  care  of 
the  men. 

ON    THE    LINE. 

Don't  let  your  leveler  get  too  far  behind  the  transit  work,  and 
see  that  he  checks  his  levels  and  establishes  benches  at  proper 
intervals.  After  the  work  is  well  started  you  will  be  obliged  to  go 
ahead  and  make  yourself  familiar  with  the  features  of  the  country 
and  select  the  points  where  your  line  must  be  run.  A  preliminary 
line  is  usually  run  without  curves,  and  the  work  of  the  transitman 
is  much  easier  than  in  location  surveys,  and  the  line  work  is  much 
more  easily  carried  on  than  when  locating ;  and  this  brings  us  to 
the  work  of  the  transitman.  But  before  leaving  this  part  of  the 
subject  let  me  remind  you,  that  as  your  work  progresses,  you  will 
have  to  come  in  contact  with  the  property  holders  and  residents  of 
the  country,  and  you  should  always  bear  in  mind  that  you  repre- 
sent large  interests  and  can  give  them  by  your  manner  a  favorable 
or  unfavorable  impression  as  you  choose. 

THE    TRANSITMAN. 

The  transitman  has  the  hardest  work  of  the  party  to  perform ; 
he  has  to  stand  with  one  eye  at  his  instrument  as  long  as  the  men 
can  set  stakes,  and  then  when  he  is  called  up,  the  whole  chain  and 
axe  force  have  to  be  idle  till  he  arrives  at  the  place  where  they  are 


48  ENGINEERING  FIELD  WOKR. 

and  has  set  up  and  lined  his  instrument ;  he  is  supposed  to  direct 
the  work  in  the  absence  of  his  superiors,  to  know  the  topography 
of  the  country  ahead  and  run  his  line  to  suit  the  ground— to  keep 
all  the  men  at  work  and  not  let  them  loaf  around — to  keep  all 
notes,  and  if  possible  sketch  all  the  topography;  to  act  as  chie 
assistant  in  every  way,  to  be  book-keeper  and  cashier  of  the  party ; 
if  in  camp,  to  purchase  supplies  and  see  that  things  go  right  gen- 
erally. The  skill  of  the  transitman  in  the  field  consists  in  his 
realization  of  the  peculiar  features  of  the  ground  and  his  judgment 
in  running  to  them,  and  to  his  being  able  to  work  under  mental 
pressure.  The  mere  instrumental  work  in  a  preliminary  survey  is 
easy  to  do,  as  it  consists  only  in  running  bearings,  noting  angles 
and  giving  the  line  to  the  men  at  the  chain.  A  few  words  to  the 
transitman:  Carry  your  instrument  yourself;  don't  let  any  of  the 
men  take  it  at  night  unless  you  are  just  ready  to  drop  with  fatigue. 
Your  men  may  very  probably  offer  to  carry  your  instrument,  as  a 
common  courtesy,  or  even  to  make  friends  with  you,  but  don't 
accept  such  favors ;  among  working  men,  from  which  class-  your 
chainmen  and  axemen  will  most  probably  come,  there  is  but  one 
standard  of  comparison,  and  that  is  strength,  and  although  one  of 
them  may  be  perfectly  willing  to  shoulder  your  fifteen  pound 
transit  for  three  or  four  miles,  you  will  not  gain  his  respect  by 
letting  him- do  it  for  you.  If  you  have  not  strength,  make  up  for  it 
in  endurance  and  quiet  pluck,  and  if  you  want  to  grumble,  don't  do 
it  before  the  men.  You  and  the  engineer-in-charge  must  be  in 
perfect  accord,  at  least  in  appearance,  if  you  want  to  further  the 
interests  of  your  employers  and  your  own  also.x  In  setting  up  a 
transit  on  sideling  ground  it  is  generally  better  to  put  one  leg  of 
the  tripod  up  hill  and  two  down,  but  you  must  exercise  a  little 
common  sense  in  the  matter;  try  to  keep  the  lower  "parallel 
plate  "  as  level  as  possible,  as  by  so  doing  time  in  "  leveling  up  " 
will  be  saved ;  try  to  make  yourself  master  of  your  instrument  as 
there  is  a  great  range  in  the  value  of  transitmen,  and  try  to  "set 
up  "  each  time  a  little  quicker  than  before,  and  also  a  little  better. 
The  acme  of  setting  a  transit  may  be  considered  reached  when  one 
shove  on  each  leg  of  the  tripod  brings  the  "plumb-bob"  exactly 
over  the  point  in  the  stake,  while  the  instrument  is  found  level 
"both  ways.'^  Try  and  see  how  many  times  you  can  do  this  every 
day,  but  don't  waste  time  studying  how  to  do  it  at  each  "  set."  It 
is  rather  better  to  keep  the  plates  clamped  together  at  zero,  and  do 
all  lining  of  the  instrument  with  the  lower  clamp  and  tangent ; 


THE  LEVELEB— LEVELING.  49 

take  bearings  on  both  fore  and  back  sights  as  you  may  detect 
errors  in  reading  angles  by  so  doing,  and  be  careful  to  record 
which  way  angles  are  turned.  It  is  most  convenient  to  run  your 
transit  ahead  always  and  read  the  same  end  of  the  needle  if  the 
instrument  is  in  as  good  adjustment  as  it  should  be.  The  stability 
of  the  adjustment  differs  very  widely  in  different  instruments.  We 
have  worked  with  an  instrument  for  three  months  which  never  had 
to  be  touched,  and  also  with  another  from  the  same  maker  which 
would  not  reverse  truly  for  the  day,  although  adjusted  every 
morning ;  it  becomes  necessary,  therefore,  to  learn  the  peculiarities 
of  your  instrument,  and  know,  not  guess  at,  its  condition  at  all 
times.  The  reversal  should  be  tested  each  morning  before  going 
to  work  until  you  are  sure  of  the  instrument.  Learn  which  way  to 
get  the  slack  of  the  tangent  screws,  and  to  do  good  work  with  a  poor 
transit. 

THE    LEVELER. 

The  leveler  on  a  preliminary  survey  may  have  to  work  at  his  best 
to  keep  up  with  the  transit  party,  and  as  the  leveler  and  rod  man 
have  to  work  completely  in  unison,  we  will  give  them  our  advice 
together  after  their  field  work.  Of  course,  in  the  office,  or  in  camp 
they  are  two  very  different  people,  the  leveler  being  one  of  the 
commissioned  officers  of  the  party,  if  we  may  use  a  military  term, 
while  the  rodman  is  about  the  grade  of  a  sergeant  only.  Still  there 
should  be  very  little  difference  of  feeling  between  them.  The 
leveler  keeps  all  field  notes  and  the  rodman  should  also  carry  a 
book  and  keep  the  turning  point  sights  and  work  out  all  heights  of 
the  instrument  and  elevations  of  turning  points  and  benches  in  t  e 
field.  Readings  for  turning  points  and  benches  may  be  taken  to  the 
thousandths,  but  for  station  heights  the  nearest  tenth  only  should 
be  read. 

LEVELING. 

i  »  « 

Make  all  the  vertical  height  you  can  in  going  up  or  down  hill 
as  you  may  save  a  setting  thereby.  Study  the  ground  as  to  what  is 
coming  ahead  and  never  select  turning  points  or  set  up  the  instru- 
ment without  having  fully  considered  what  is  to  be  done  next. 

Be  sure  of  the  adjustments  of  the  instrument  and  that  the  rod  is 
held  "plumb  "  (if  the  cross  hairs  are  right,  the  man  at  the  instru- 


$0  3ENOINEEBING  FIELD  WOKE. 

ment  can  see  by  the  vertical  hair  if  the  rod  is  "plumb-"  one  way, 
and  by  gently  swinging  the  rod  in  the  plane  of  the  instrument  after 
setting  the  target  if  the  target  rises  above  the  hair,  the  rod  was 
not  held  "plumb;"  if  the  target  on  swinging  the  rod,  falls  below 
and  just  comes  up  to  the  hair,  the  rod  has  been  held  vertically). 
Make  your  signals  with  some  system,  and  move  the  rod  according 
to  the  signal  in  amount  of  motion  as  well  as  direction,  speak  your 
numbers  distinctly  and  don't  mistake  the  word  seven  for  eleven,  or 
the  reverse. 

Leveling  can  be  hurried  in  open  country  by  employing  two  rod- 
men  and  rods,  and  running  them  alternately,  the  employment  of 
a  fourth  man  to  keep  notes  in  such  case  being  a  great  help, 
although  such  great  haste  is  not  often  required  or  desirable.  ( 

Put  in  benches  at  least  once  in  1,500  feet  in  open  country,  and 
every  1,000  feet  in  rough  country,  as  it  may  save  you  a  good  deal  of 
work;  select  good  points  for  benches  and  turning  points,  and 
always  be  sure  that  the  instrument  may  be  moved  before  you  move 
it," and  that  you  can  find  at  least  half  of  the  turning  points  in  the 
day's  work. 

In  running  "  check  levels  "  check  up  the  benches  every  mile,  and 
if  the  agreement  is  within  one-tenth,  call  bench  right  and  go  on. 
Try  to  keep  the  check  levels  within  two  miles  of  each  other;  as  it 
may  save  a  good  deal  of  annoyance. 

The  work  of  the  rest  of  the  party  is  much  the  same  for  location 
and  preliminary  surveys,  and  will  be  described  further  on.  The 
engineer  in  charge  of  the  party  and  the  transitman  are  the  ones 
whose  work  is  increased  the  most,  and  their  duties  will  be  described 
again  for  location  survey. 

THE    HEAD    CHAINMAN. 

The  head  chainman  holds  an  important  position  and  must  be  a 
man  with  sound  judgment,  and  must  understand  his  work.  He 
should  hold  the  transit  rod  with  one  hand,  and  the  chain  with  the 
other,  showing  discretion  as  to  holding  the  chain  level  and  taking 
short  lengths  on  hilly  ground ;  he  should  understand  the  signals 
of  the  transitman  and  obey  them  intelligently ;  should  have  a  good 
eye  for  line  and  use  it  every  time  he  holds  his  rod  up,  so  as  to  be  as 
nearly  right  as  may  be  before  the  transitman  begins  to  signal  to 
him ;  and  he  should  always  look  at  the  transitman  when  lining, 
instead  of  gazing  around  at  other  things.  His  work  is  perhaps  best 
conducted  in  the  following  order:  When  the  chain  is  pulled  out 


HEAD  CHAINMAN-TRANSIT  POINTS.  51 

he  turns  around,  and  holding  the  rod  with  one  hand,  tries  to  place 
it  as  nearly  correct  as  he  can  by  lining  over  the  last  stake  to  the 
instrument,  while  with  the  other  hand  he  is  trying  to  "  straighten 
out  the  chain ;"  he  then  moves  the  rod  in  obedience  to  the  motions 
of  the  man  at  the  instrument,  and  after  getting  the  line,  holds  the 
chain  up  to  the  rod  with  both  hands  and  gets  the  distance ;  then 
dropping  the  chain  he  stands  up  straight,  plumbs  the  rod  carefully 
and  receives  the  line  again  ;  then  pressing  the  rod  into  the  ground 
he  makes  the  hole  with  the  point,  and  takes  it  off  the  ground :  a 
stake  is  then  driven  and  the  measurement  should  be  repeated  to 
see  if  the  distance  is  correct,  after  which  the  rod  is  held  on  the  stake 
"  for  line,"  the  chain  is  then  dragged  on  and  the  operation  repeated. 
Time  may  be  lost  by  neglecting  the  order  of  operations  given  above, 
or  by  not  looking  to  see  where  the  line  is,  and  leaving  all  the  move- 
ments to  be  signalled  from  the  instrument,  or  by  jerking  the  chain 
while  trying  to  straighten  it,  or  by  not  watching  the  transitman 
closely,  and  thus  missing  his  signals.  If  you  are  so  far  away  that 
the  motion  cannot  be  seen,  take  your  handkerchief  or  hat  and 
make  a  signal  (imitating  the  lining  signals)  and  the  transitman  will 
understand  that  you -wish  him  to  take  his  handkerchief,  (when 
snow  is  on  the  ground,  his  hat)  to  increase  the  visibility  of  his  sig- 
nal. Remember  that  the  transitman  can  see  you  plainly,  and  can 
guess  what  you  may  wish  him  to  do.  When  you  wish  him  to  line 
you  hold  up  your  rod  and  wave  it  to  catch  his  eye,  and  when  you 
are  sure  that  the  line  can  go  no  further  without  a  change  in  the 
position  of  the  instrument,  you  must  call  his  attention  by  holding 
your  rod  in  both  hands  horizontally  above  your  head ;  then  after 
carefully  lining  and  centering,  you  can  call  him  up  by  beckoning 
with  both  hands,  holding  the  rod  above  your  head  or  by  any  other 
previously  arranged  signal. 

SELECTION    OF    TRANSIT    POINTS. 

By  far  the  most  important  duty  in  point  of  difficulty,  is  the  selec- 
tion of  the  transit  points,  which  must  be  so  chosen  that  the  greatest 
distance  ahead  may  be  seen  from  them  ;  in  general  they  should  be 
on  the  upper  edges  of  hills,  where  a  view  of  the  valley  on  both 
slopes  can  be  obtained,  and  if  possible,  where  a  full  view  of  the  tran- 
sit rod  can  be  had,  as  it  is  only  allowable  in  case  of  necessity  to 
sight  at  but  a  small  part  of  the  rod,  and  therefore  great  care  must 
be  taken  to  hold  "plumb"  at  all  times,  as  you  do  not  know  just 
bow  much  of  the  rod  may  be  observed,  You  must  exercise  consicU 


52  ENGINEEKING  FIELD  WOEK. 

erable  judgment  in  the  matter,  and  never  be  astonished  if  your 
views  and  the  transitman's  differ  on  this  point.  And  here  let  us 
say  a  word  to  all  the  men ;  remember  that  the  transitman  has  to 
work  all  the  time,  and  that  he  has  to  take  all  the  blame  from  the 
engineer-in-charge  for  all  mistakes,  and  that  if  he  does  scold  you 
for  things  that  are  not  your  fault,  just  wait  till  the  matter  devel- 
opes,  but  do  not  try  to  argue  during  working  hours  about  the  work ; 
if  you  have  been  to  blame,  you  deserve  "jawing,"  and  if  you  have 
not,  it  will  not  hurt  you  a  bit  in  the  eyes  of  anybody  whose  opinion 
is  worth  having.  The  same  remarks  will  apply  to  the  transitmen 
and  levelers  in  their  relations  to  their  superior ;  let  them  remember 
that  the  engineer-in-charge  has  more  things  to  think  about  in  a  day 
than  they  have  in  a  week,  and  if  they  don't  believe  it,  wait  until 
they  have  the  same  position  and  can  see  for  themselves. 

THE    BEAB    CHAINMAN. 

The  work  of  the  rear  chainman  is  to  hold  the  chain  while  it  is 
being  pulled  along ;  we  say  hold  it,  for  if  you  let  the  end  go  you  may 
have  to  call  the  front  chainman  back  for  10  or  20  feet  after  he  has 
passed  his  proper  distance,  and  he  won't  like  that.  Don't  hang 
on  the  chain  and  be  dragged  by  it,  but  be  ready  to  give  it  a  shake 
and  clear  it  if  it  catches  on  brush  or  rocks.  The  rear  chainman  is 
responsible  for  the  numbering  of  the  stakes,  and  for  all  distances 
with  "plus  "  numbers;  he  must  be  careful  to  assist  in  straighten- 
ing the  chain,  to  be  on  hand  promptly  in  measuring,  and  not  get  in 
the  line  nor  walk  on  the  line,  and  not  to  jerk  the  front  chainman 's 
arms  off  by  suddenly  stopping.  The  keeping  of  the  numbers  right 
is  a  more  difficult  task  than  it  seems  to  be,  and  requires  a  good 
memory ;  in  all  cases  of  doubt,  go  back  and  find  out  at  the  last 
stake  what  is  right  and  don't  guess  at  it.  Be  careful  that  the  chain 
is  in  good  order — that  the  links  are  straight  and  that  the  rings  are 
not  pulled  open.  Do  it  up  from  the  handle  and  keep  the  strap 
around  it ;  learn  to  throw  a  chain  over  a  stream ;  one  end  of  an 
ordinary  heavy  chain  can  be  thrown  over  a  50  feet  stream.  And  by 
making  two  bundles  with  say  15  feet  between  them,  and  using  two 
men  to  throw,  one  after  the  other  (at  say  half  a  second  interval),  we 
have  thrown  the  end  of  a  heavy  chain  75  feet.  Be  careful  that  the 
chain  is  not  dragged  against  the  transit  legs,  and  do  not  hit  them 
while  trying  to  stand  the  straightening  as  inflicted  by  the  head 
chainman;  be  prompt  to  assist  in  making  short  chains  on  hilly 
ground,  and  on  curves,  if  there  are  any,  and  wal  k  the  outer  side 


AXEMEN— LOCATION— CARELESSNESS,  ETC.  53 

of  the  line  lest  you  get  in  the  ''line  "  of  the  instrument  without 
knowing  it. 

THE  AXEMEN. 

The  axemen  are  under  the  general  direction  of  the  head  chain- 
man  who  gives  the  line  for  cutting  brush  and  timber  with  his  rod. 
One  axeman  must  be  in  charge  of  the  stakes  and  must  never  let  the 
chain  work  wait  for  him  a  second,  but  must  keep  up  at  all  risk. 
Sometimes  a  large  basket  is  useful  in  carrying  stakes.  The  stakes 
should  be  numbered  by  the  chainman,  and  if  he  marks  a  number 
of  them  in  the  basket,  care  must  be  taken  to  see  that  in  "plus  " 
stations  the  numbered  stakes  are  not  used,  or  the  numbers  may 
get  "  mixed." 

LOCATION. 

In  location  surveys  the  only  difference  in  the  work  of  the  men  is 
in  the  curve  work,  where  the  head  chainman  has  to  offset  from 
the  line  of  the  last  stake  to  find  the  transit  "line  "  by  an  amount 
known  as  the  chord  "deflection,"  for  which  see  "Henck's  Field 
Bock."  We  always  gave  the  chainraan  a  list  of  "  chord  deflections  " 
for  the  even  degrees,  and  let  him  guess  at  the  amount  of  the 
ground,  and  found  that  it  saved  time.  The  centering  of  the  stakes 
should  be  attended  to  a  little  more  carefully  than  on  preliminary 
work,  and  the  measurements  made  with  more  care. 

A  back  rodman  will  be  necessary,  and  we  can  only  caution  him 
to  stand  up,  with  his  rod  in  position  all  the  time,  or  if  near  enough 
to  see,  whenever  the  transitman  turns  over  his  telescope,  he  must 
be  on  hand.  Although  the  job  is  not  very  interesting  it  is  impor- 
tant. We  used  to  let  the  back  rodman  carry  the  coats,  and  if  we 
took  our  dinner  along,  a  basket  with  the  "  grub." 

Each  man  in  the  party  must  be  held  strictly  responsible  for  what 
tools  or  instruments  are  put  into  his  hands,  and  a  careful  property 
account  must  be  kept  and  reported  from  time  to  time. 

WASTEFULNESS  OF  CARELESS  LOCATION. 

Location  surveys  differ  from  preliminary  surveys  in  being  more 
carefully  carried  out,  as  to  the  exact  position  of  the  line,  and  in  the 
curve  running,  which  is  usually  omitted  on  the  preliminary  work. 
The  exact  position  of  the  line  is  a  matter  of  great  importance,  for 
many  dollars  are  thrown  away  by  careless  locations  and  in  many 
cases  the  theory  of  wilful  ignorance  is  the  only  excuse  that  can  be 


64  ENGINEEKING    FIELD    WOKK. 

made  for  them.  There  are  needed  careful  judgment,  long  experi- 
ence, and  a  great  deal  of  real  hard  work  on  the  part  of  the  engineer 
in  charge  of  the  locating  party,  to  make  successful  locations. 

THE  TOPOGRAPHER. 

The  party  is  usually  organized  with  the  same  force  as  in  the  pre- 
liminary survey,  viz :  An  engineer-m-charge,  transitman,  leveler, 
level  rodman,  two  chainmen  and  from  one  to  five  axemen.  To 
these  are  often  added  a  topographer,  and  sometimes  a  cross-section 
leveler  and  helper  or  rodman.  The  topographer  takes  sketch-notes 
of  the  contours  and  surrounding  country,  roads,  buildings  etc., 
which  have  to  be  shown  in  the  plans,  and  if  he  carries  a  pocket 
"  azimuth  compass,"  or  a  pocket  sextant,  he  will  find  it  a  great  help 
to  him,  but  for  his  work  we  especially  recommend  a  small  plane 
table,  18  inches  square,  with  the  paper  on  it  in  "  block  "  fashion,  the 
board  fitted  with  a  shoulder  strap,  and  Jacob  staff  mountings,  and 
a  folding  "alidade  "  or  ruler,  with  sights.  With  this  outfit  a  topo- 
grapher can  produce  a  line  map  which  will  make  his  chief 
engineer's  heart  glad,  and  which  will  go  a  long  way  towards  con- 
vincing the  directors  that  the  party  have  done  a  lot  of  work.  Th« 
use  of  the  plane  table  for  this  purpose  is  not  common,  but  such  an 
arrangement  costs  very  little,  and  nothing  else  will  show  as  much 
of  the  country  in  a  very  short  time.  The  field  use  of  the  instrument 
is  very  simple ;  the  line  already  run  being  platted  before  taking  the 
field,  the  "  orientation  "  can  be  performed  from  stakes  and  it  can  be 
used  anywhere. 

The  cross-section  leveling  is  only  performed  in  very  rough  coun- 
try ;  a  10-foot  pole  with  a  short  spirit  level  placed  on  it,  and  then 
held  witli  one  end  on  the  ground  and  the  other  against  a  graduated 
rod  on  which  the  rise  or  fall  in  10  feet  is  noted,  is  used ;  the  infor- 
mation obtained  in  this  way  is  very  considerable ;  there  is  a  good 
deal  of  work  to  get  it  but  the  men  are  not  required  to  have  a  very 
high  grade  of  mental  organization  and  do  not  draw  a  very  high 
pay. 

ENGINEER  IN  CHARGE. 

All  of  the  increased  care  and  skill  required  and  already  men- 
tioned has  to  come  from  two  men — the  engineer-in-charge  and  the 
transitman — the  former  has  all  the  responsibility  of  the  added  im- 
portance of  the  survey,  and  the  constant  study  of  the  ever  changing 
ground,  and  the  greater  or  less  difficulty  of  the  work  itself ;  and 


ENGINEER   IN    CHARGE— TRANSIT   NOTES.  55 


the  latter  has  all  the  curve  work,  with  increased  watchfulness 
and  greater  accuracy,  to  attend  to ;  those  two  men  have  their  work 
nearly  doubled,  while  the  work  of  the  rest  of  the  party  is  only  in- 
creased by  the  additional  care  and  attention  which  has  to  be 
enforced  on  all  the  party. 

To  the  engineer-in-charge  we  shall  say  very  little,  and  to  a  man 
in  that  position  little  can  be  said — if  he  does  not  know  his  business 
he  certainly  ought  not  to  be  in  the  place,  and  if  he  does  know  it, 
our  advice  is  unnecessary,  yet  if  he  does  not  think  it  beneath  him 
to  read  what  we  have  to  say  to  transitmen,  he  may  here  and  there 
find  a  hint  to  help  him  in  watching  the  work  of  that  indispensable 
assistant.  And  here  let  us  say  that  no  money  is  ever  sa.ed  by 
making  the  engineer-in-charge  of  the  location  run  either  transit 
or  level,  as  he  needs  all  of  his  faculties  to  be  at  all  times  shar- 
pened to  their  utmost  degree  to  attend  to  his  own  duties,  and  if  the 
tedious  instrumental  work  is  put  upon  him  he  cannot  keep  every- 
thing going  at  once  properly.  And  let  us  say  also,  that  if  the 
engineer-in-charge  wishes  to  make  every  man  do  his  very  utmost, 
that  he  had  better  take  the  head  of  the  chain  himself  when  he  can 
spare  the  time,  especially  on  long  tangents,  which  he  has  already 
determined.  By  so  doing  he  will  be  near  all  the  men  of  the  transit 
party,  and  they  will  work  when  they  are  right  under  the  eye  of  the 
"  boss,"  and  he  will  be  sure  that  no  time  will  be  lost  in  picking  out 
the  transit  stations,  and  that  the  stakes  are  kept  well  up;  the 
transitman  will  always  hurry  up  to  him,  and  if  he  cannot  keep 
them  all  "  on  the  jump,"  he  is  not  fit  for  his  place.  Of  course,  he 
has  frequently  to  go  ahead  and  pick  out  the  ground,  and  go  back 
to  see  how  the  profile  will  plat,  and  tell  the  transitman  what  must 
be  done  in  his  absence,  and  in  this  he  must  be  his  own  judge  of  his 
time  and  of  its  disposition,  but  still,  when  he  wishes  to  drive 
matters,  he  can  do  so  best  from  the  head  of  the  chain,  in  the 
meantime  letting  the  head  chainman  take  the  transit  rod  and  keep 
up  the  centers ;  the  mental  work  which  he  has  to  perform  all  the 
time  will  not  suffer  from  the  mere  manual  labor  of  being  head 
chainman. 

KEEPING  TRANSIT   NOTES. 

The  transitman  has  after  all  a  hard  place  to  fill,  for  there  is  no 
variety  in  his  mental  work ;  he  has  to  keep  a  sharp  watch  on  the 
men  when  his  superior  is  absent,  and  has  the  constant  computa- 
tion of  deflection  angles  to  attend  to  on  curves,  at  the  same  time 


56 


ENGLNEEBING    FIELD    WOKK. 


using  all  possible  diligence  as  to  figures.  And  here  a  hint  as  to 
the  easiest  way  of  keeping  the  curve  notes  and  doing  the  transit 
work.  The  method  originated  we  know  not  how,  and  may  have 
have  been  used  by  large  numbers  of  transitmen,  although  we  have 
never  happened  to  meet  them. 

The  basis  of  all  circular  curve  work  with  the  transit  is  the  well 
known  theroem :  the  angle  between  a  tangent  chord,  or  between 
any  two  chords  which  meet  at  a  point  on  the  curve,  is  measured  by 
half  the  intercepted  arc.  And  as  the  point  where  the  chords  meet 
on  the  curve  may  be  anywhere  on  that  curve,  it  follows  that  the 
sum  of  any  consecutive  angles  or  series  of  angles  is  the  same  no 
matter  where  the  instrument  be  placed  on  the  curve  for  given 
arcs,  and  that  if  the  deflection  angles  be  all  computed  from  the  B. 
C.,  as  far  as  may  be  desired,  at  any  station  on  the  curve  the  number 
can  be  used,  as  the  differences  will  be  the  same  for  the  same 
stations.  To  illustrate  this,  we  must  assume  an  example. 

Let  it  be  required  to  run  a  five  degree  .curve  from  sta.  131  -f  40, 
and  let  us  first  look  at  a  page  in  a  field  book : 


STATIONS. 


DEFLEC-  I    CUEVE. 
TIONS. 


TEUE  COUESE. 


NEEDLE 
COUESE. 


129 

N  16}o  W 

N  16°.  W 

130 

B.  C.  +40 

0°0' 

5°E. 

N  16°15'  W 

2 

1°30' 

3 

4°0' 

4 

6°30' 

5 

9°0' 

«N  +50 

10°  15' 

6 

11°30' 

7 

14°0' 

^   8 

16°30' 

E.  C.  +25 

17°7| 

34°15' 

N  18°  0'  E 

N  17f  °  E 

We  see  the  book  is  ruled  with  five  columns  and  usually  on  the 
left  hand  page,  the  right  hand  page  being  reserved  for  "remarks." 
The  column  for  Stations  explains  itself,  the  signs  ''plus"  being 
used,  decimal  points  for  a  hundred  foot  unit,  and  the  ordinary 
"decimal"  being  reserved  for  feet  and  fractions  of  feet.  The 
letters  B.  C.  and  E.  C.  are  used  for  beginning  and  end  of  the  curve* 
instead  of  the  P.  C.  and  P.  T.  used  often  for  "  point  of  curve  "  and 
"point  of  tangent,"  being  more  in  accordance  with  the  usage  of 
ordinary  geometry  and  has  been  our  custom  for  several  years. 


KEEPING    TRANSIT    NOTES.  57 

The  column  of  deflections  contains  the  deflection  angles  com- 
puted from  B.  C.  as  far  as  convenient,  say  to  station  135,  ana  the 
stakes  set  and  centered,  for  same  reason  135  +  50  becomes  necessary 
and  has  to  be  put  in ;  then  the  transit  is  turned  back  to  0°  and 
turned  over  on  the  back  sight  to  be  sure  that  nothing  has  slipped 
and  carried  up  to  135-1-50,  and  set  up.  The  instrument  is  then  set 
a*;  0°  and  sighted  at  B.  C.  and  then  if  turned  to  10C  15'  it  would  be 
on  the  tangent  at  135+50,  and  if  turned  to  11°  30',  it  will  be  on  the 
chord  from  135  +  50  to  136,  and  by  adding  these  2°  30'  for  each  hun- 
dred feet  the  curve  is  run  to  138  and  the  transit  is  moved  to 
that  place  after  taking  a  back  sight  as  before,  with  the  plates  at 
0°.  After  setting  up  at  138  if  we  could  see  B.  C.  we  should  set  at 
0°  again,  and  turning  to  16°  30'  we  would  be  on  the  tangent ;  but  B. 
G.  is  supposed  invisible,  and  we  shall  therefore  set  the  instrument 
at  10°  15'  and  sight  it  back  at  135  +  50  and  the  result  is  that  the 
lower  plate  is  in  the  same  position  as  if  B.  C.  had  been  visible,  and 
we  had  as  above  suggested  set  0°  and  sighted  thereat;  by  turning 
to  16°  30'  we  shall  be  on  the  tangent  at  130  and  if  we  find  that  1°  20' 
more  will  be  needed  to  strike  the  desired  direction  from  there,  we 
will  put  1°  15'  more  in  the  curve  or  37|'  deflection  which  corresponds 
to  25  feet ;  we  run  out  the  25  feet  and  turn  tolO£'  and  sight  the  stake 
in,  and  then  turning  to  10°15',  we  turn  over  to  the  back  sight ;  af- 
ter satisfying  ourselves  that  it  is  all  right,  we  go  to  138  +  25  and 
being  sure  the  instrument  reads  10°15,  we  sight  again  at  135  +  50 
and  turn  to  17°7J'  and  are  at  the  tangent.  By  taking  the  differences 
and  comparing  distances  it  will  easily  be  seen  that  the  angles  are 
all  right. 

Now  in  what  does  this  method  consist  that  is  better  than  the 
practice  of  counting  stations  and  multiplying  by  the  deflection 
angle  ?  Only  this,  that  the  counting  and  multiplication  are  both 
performed  already.  Each  station  is  attached  to  the  angle  opposite 
to  it  in  the  note  book,  and  once  there  it  is  good  for  all  the  work 
that  you  can  do  with  it.  The  mental  labor  thus  saved  is  a 
great  help.  It  was  once  our  fortune  to  have  to  "  break  in  "  two 
"green"  transitmen  in  five  weeks,  and  in  all  that  time  we  com- 
puted every  angle  that  was  used  at  the  instrument,  mentally, 
and  kept  at  the  head  of  the  chain  most  of  the  time ;  by  asking 
the  man  at  the  instrument  what  reading  he  had  and  what  station 
he  was  at  and  what  his  back  rodman  was  at,  we  never  let  a  mistake 
pass  our  notice.  (Note.— We  are  not  anxious  to  repeat  this  experi- 
ence of  our  transit  running  from  the  head  of  the  chain.) 


58  ENGINEEKING    FIELD    WORK. 

For  the  transitman  himself  this  system  of  notes  is  a  great  relief 
as  he  is  free  from  the  constantly  recurring  question  "what  is 
your  next  deflection?"  with  its  importunate  worrying  when  he 
has  just  setup  on  an  odd  "plus"  and  knows  that  his  back  rod- 
man  is  also  on  an  odd  "plus,"  he  simply  asks  himself,  what  are 
the  readings  for  these  two  stations  knowing  that  the  difference 
between  them  has  been  computed  carefully  once  as  they  come 
along,  and  it  will  be  all  right  now. 

COMPOUND  CUBVES. 

On  compound  curves  the  same  method  can  be  followed  all  around, 
but  the  back  rodman  and  the  instrument  must  be  on  the  same 
branch  ( the  P.  C.  0.,  point  of  compounding  of  curve,  is  of  course  on 
both  branches).  The  next  column  of  the  note  book  is  headed 
"curves"  and  in  it  are  recorded  the  degree  and  direction  of  the 
curves  and  the  central  angle,or  angle  of  intersection ;  it  is  twice  the 
last  deflection  angle  always.  In  the  next  column  is  put  up  the  com- 
puted curves  from  the  first  one,  and  the  next  one  contains  the 
needle  readings;  the  use  of  these  is  a  check  to  the  transitman 's 
work  and  sudden  variations  are  not  common.  If  "  local  attraction  " 
exist,  it  can  be  found  by  reading  the  compass  at  each  end  of  the 
tangent.  We  remember  a  local  attraction  which  bothered  us  all 
one  morning  and  which  never  seemed  to  be  the  same  for  two  min- 
utes running,  and  which  quite  frightened  our  "  boss  "  but  as  ve 
were  within  fifty  feet  of  a  north  and  south  track,  we  talked  "  earth 
currents  "  at  him  (they  were  east  and  west)  and  as  we  were  sure  of 
our  work  we  let  it  go  unexplained ;  in  the  afternoon  we  discovered 
the  innocent  cause  to  be  a  small  "  Smith  &  Wesson  "  in  our  over- 
coat breast  pocket,  and  we  have  never  seen  any  such  local  attrac- 
tion since. 

LONG  TANGENTS. 

Long  straight  lines  require  a  good  deal  of  care,  and  the  instru- 
ment should  be  reversed  "  both  ways  "  on  them,  and  if  a  long  sight 
can  be  obtained  backward  so  as  to  overlook  two  or  three  transit 
points,  they  should  be  tested  by  the  direct  instrument.  If  great 
care  is  needed,  the  instrument  should  be  used  "both  wavs  "  without 
reversing,  and  the  slack  of  the  clamp  screws  watched.  Tangent 
screws  are  now  so  generally  made  double  that  the  play  of  the 
motion  screws  can  be  prevented  from  interfering  with  the  ac* 


COMPOUND    CUBVES-LONG    TANGENTS.  59 

curacy  of  the   work,   but  the  clamps   will  wear  loose  a  little  and 
must  be  watched. 

LAND    LINES. 

In  Eailway  field  work,  after  the  location  survey,  follows  legi- 
timately the  land  surveyor  "land  lines"  as  they  are  called 
in  the  east,  and  although  most  of  this  work  is  included  in  com- 
mon surveying,  yet  there  are  some  points  of  difference  which  it  will 
be  well  to  touch  upon.  In  cities  and  towns  where  land  is  valuable, 
it  is  of  course  quite  important  to  have  the  work  done  accurately ; 
and  although  in  the  western  country,  where  the  land  is  very  com- 
monly given  to  the  railroad  company  it  is  not  so  essential,  still  it  is 
always  desirable  to  know  how  to  do  good  work,  and  a  few  words  as 
to  general  surveying  will  scarcely  be  out  of  place. 

In  the  first  place  be  sure  that  your  work  is  definitely  connected 
with  points  which  can  be  found  again,  and  that  the  connection  with 
the  main  line  is  right,  and  that  it  is  simple ;  any  complex  mea- 
surement is  to  be  avoided.  In  the  next  place,  measure  every  dis- 
tance pertinent  to  the  work  which  can  be  directly  measured.  Cal- 
culate as  little  as  possible.  If  the  land  to  be  taken  is  very  irregular 
in  form,  a  "  traverse  "  is  the  best  method  of  attack  if  all  the  sides 
can  be  measured;  don't  have  any  "  omissions "  to  supply  if  you 
can  help  it ;  be  careful  to  take  all  offsets  at  right  angles ;  take  the 
angles  with  a  transit  if  one  can  be  had,  and  do  not  use  the  com- 
pass in  any  way  but  as  a  check  on  the  transit ;  for  sighting  right 
angles  quickly,  some  of  the  forms  of  the  "  optical  square  "  may  be 
found  very  convenient ;  for  ordinary  work  in  cities  most  of  the 
measurements  for  land  will  be  at  right  angles  or  nearly  so,  and 
the  work  oan  be  laid  out  on  four  lines  forming  a  trapezium ;  do  not 
trust  to  any  building  for  a  right  angle  or  to  any  two  walls  of  the 
same  building  to  have  parallel  faces ;  brick  laying  is  not  by  any 
means  the  most  exact  of  trades,  and  although  for  a  map  the  errors 
will  not  show,  yet  for  other  work  to  be  connected  to  that  in  progress, 
it  may  lead  to  serious  errors. 

For  railroad  purposes  the  land  is  usually  found  in  long  narrow 
strips  of  varying  width ;  and  it  is  sufficient  to  find  the  length  on  the 
centre  line,  and  directions  of  bounding  lines  which  cross;  it  is 
however,  desirable  to  have  all  "land  lines"  within  four  or  five 
hundred  feet  of  the  track,  and  this  requires  measurements  on  the 
crossing  lines.  In  getting  the  direction  of  a  fence,  when  the  instru- 


60  ENGINEERING    FIELD    WORK. 

ment  is  placed  at  one  side,  measure  the  distance  from  the  instru- 
ment to  the  fence  at  right  angles  to  it  and  have  a  similar  "offset'1 
made  as  far  as  possible  from  the  instrument ;  of  course  the  main 
tine  should  have  been  run  and  the  transit  placed  in  the  line  before 
the  direction  can  be  obtained. 

For  street  surveying  the  best  method  is  that  of  a  line  in  the  mid- 
dle, with  offsets  and  measurements  connecting,  the  offsets  at  the 
end  as  well  as  the  line  run.  In  very  crowded  streets  we  have  some- 
times run  a  line  down  each  footwalk,  connected  them  carefully  at 
their  ends,  and  then  proceeded  as  described  for  a  single  line. 

CAREFUL  NOTES 

In  all  work  of  this  kind  the  most  important  thing  is  to  take  good 
notes ;  always  put  these  down  as  if  you  expected  to  die  before 
morning,  and  wanted  to  leave  them  in  such  good  condition  that  in 
ten  years  time  a  stranger  with  no  previous  acquaintance,  and  with  no 
one  of  the  old  party  to  help  him,  could  take  your  book  and  proceed 
on  the  job  without  delay ;  if  this  can  be  done,  your  notes  must  be 
about  right,  but  you  never  will  have  them  too  complete.  We  have 
never  used  any  but  the  "sketch  system  "  for  taking  notes,  and  we 
always  made  them  in  the  field,  and  copied  them  over  on  the  next 
page  in  ink,  thus  keeping  the  rough  set  with  the  original  figures, 
and  the  finished  set  to  explain  them;  the  original  figures  have 
more  weight  as  evidence,  but  the  explanation  given  by  a  neat  ink 
copy  is  a  very  great  help  in  interpreting  them.  For  city  work  take 
all  angles  with  the  transit  more  than  once,  that  is  to  say,  "repeat 
them,"  three  or  four  times  which  is  enough ;  the  object  of  the  "  re- 
peating "  being  to  check  the  angle  and  not  to  subdivide  the  vernier 
reading. 

PRESERVING  THE  LINES 

After  the  completion  of  the  land  survey  comes  the  actual  field 
work  preparatory  to  the  construction,  and  here  it  is  customary  to 
reduce  the  number  of  men  in  the  party  and  to  begin  to  "  cut  down 
expenses  "  in  the  engineering  department. 

The  first  thing  to  be  done  is  to  "  preserve  "  the  line,  that  is,  to  con- 
nect all  tangent  points  with  stakes  that  are  away  from  the  line  and 
far  enough  from  it  not  to  be  disturbed  by  the  operations  of  grading" 
and  earthwork ;  at  the  same  time  the  slope  stakes  should  be  set  and 
marked  with  the  cut  and  fill— also  the  cut  or  fill  should  be  marked 
on  the  centre  stakes— this  work  can  all  be  done  on  the  same  job,  and 


CENTRES  AND  GRADES-QUALIFICATION.  ETC.       61 

thus  the  contractors  can  make  a  start  at  once  if  they  so  wish ;  of 
course  a  record  of  all  lield  work  is  required,  and  the  results  should 
all  be  put  in  the  grade  book.  For  setting  slope  stakes  the  only  sat- 
isfactory method  is  with  the  Leveling  instrument,  though  for  com- 
paratively smooth  ground  and  light  work,  there  are  various  devices 
for  setting  slopes  which  involve  much  less  work,  and  are  sufficiently 
accurate  for  use. 

CENTRES  AND  GRADES. 

Most  of  the  work  for  railroads  in  construction  consists  in  setting 
"centres  "  and  "  grades ;"  for  the  former,  in  nine  cases  out  of  ten, 
the  line  can  be  run  in  without  an  instrument,  if  the  known  points  are 
convenient ;  the  Tangent  Deflections  are  useful  for  running  curves 
with  only  the  chain  and  rods  for  lining;  for  approximation  there  is 
a  very  convenient  method  of  computing  angles  and  distances 
(measured  as  arcs)  which  it  is  well  to  be  familiar  with  in  the  absence 
of  all  "pocket-books."  At  one  hundred  feet  distance  three-hun- 
dredths  of  one  foot  subtends  one  minute  of  arc.  Strictly  speaking  it 
is  twenty-nine  one  thousandths  instead  of  three  one  hundredths.  At 
the  same  distance  one  foot  and  three-quarters  subtends  one  degree 
of  arc,  but  one  and  eight-tenths  can  generally  be  used.  With  this 
once  fixed  firmly  in  the  mind,  mental  computations  can  be  made 
with  the  greatest  ease.  As  an  example  of  this  let  it  be  required  to 
find  Tangent  and  Chord  Deflection  for  100  feet  chord,  and  for  60  feet 
chord,  and  ordinate  at  centre  of  100  feet  chord  for  a  5°  curve :  5X1.8 
=9.00*  for  the  Chord  Deflection,  and  4  5'  for  the  Tangent  Deflection 
100  feet  chord:  4.5X0.6=2.7'— 2.7X0.6.=!. 62  Tangent  Deflection  for 
the  60  feet  chord,  and  £  of  the  Tangent  Deflection  for  100  feet  chord 
=!&'  for  the  middle  ordinate.  These  values  are  all  in  excess,  and  if 
the  deflections  are  to  be  used  for  running  the  curve  more  than  one 
station,  the  value  1|'X5=8|'  should  be  used,  and  this  is  in  error  only 
about  f  of  an  inch.  A  great  many  other  computations  may  be  thus 
performed  mentally,  and  the  work  already  done  checked  by  these 
approximations,  and  the  real  blunders  found. 

QUALIFICATIONS  FOR  LEADER. 

There  are  many  ways  of  doing  most  kinds  of  field  work,  and 
many  methods  are  described  in  the  books  under  various  heads — but 
a  good  knowledge  of  geometry  and  trigonometry,  and  possibly  a 
little  familiarity  with  analytic  geometry,  combined  with  a  cool 
head,  and  an  appreciation  of  the  external  circumstances,  will  en- 


FNGINEERING  NEWS 


AMERICAN   RAILWAY   JOURNAL. 

Published  Weekly  at  Tribu  e  Building,  N.  Y. 
Volume  XIV.,  1890. 

D.  McN.  STAUFFER.    A.  M.  WELLINGTON, 

Editors.    ' 
GEO.  H.  FROST,  Business  Manager. 

SUBSCRIPTIONS : 

To  United  States,  Canada  and  Mexico. 
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REGULATIONS 

FOR  THE 

ENGINEERING     DEPARTMENT 

DURING 

CONSTRUCTION.* 


BY  WM.  F.  SHUNK,  C.  E. 


I.   ORGANIZATION. 

1.  The  chief  engineer  will  have  exclusive  control  of  this  department. 

2.  He  may  be  aided  by  a  consulting  engineer,  without  executive  pow- 
ers, and  an  associate  engineer,  acting  under  his  immediate  direction,  to 
whom  all  official  communications  from  subordinates  should  be  addressed, 
and  whose  orders  concerning  the  work,  or  matters  thereto  appertaining, 
shall  be  received  as  authoritative. 

3.  The  associate  engineer  shall   be  aided  by  such  a  staff  of  division  en- 
gineers, principal  assistant  engineers,  draughtsmen,  clerks,  and  other 
helpers  as  shall  be  approved  by  the  chief  engineer. 

4.  Each  division  engineer  shall   have  charge  of  the  construction  of  about 
thirty  miles  of  road,  in  sections  approximating  one  mile  long  and  subdi- 
visions composed  of  from  six  to  ten  sections. 

5.  Principal   assistant  engineers  may  be  appointed  to  special  charges, 
such  as  important  structures,  the  compilation  of  records,  the  preparation 
of  plans  and  the  like.      Where  such  charges  fall  within  the  territorial 
limits  of  a  division  engineer,  strict  definition  of  responsibility  will  be  made 
and  hearty  co-operation  expected. 

*  South  Pennsylvania  B.R. 


66  ORGANIZATION-PREPARATORY  WORK. 

6.  Division  engineers  shall   have  power  to  employ  one  draughtsman  for 
the  division  headquarters  office,  and  such  resident  engineer,  inspectors, 
time  keepers,  and  other  helpers  on  the  line  of  road  as  may  be  necessary 
for  the  proper  conduct  of  the  work  for  which  they  are  immediately  re- 
sponsible, subject  beforehand  to  the  approval  of  the  associate  engineer  ; 
and  to  suspend  or  discharge  such  employes  for  sufficipnt  cause.      The 
po^er  of  removal  should  be  exercised  discreetly,  and  seldom  without 
reference  to  the  associate  engineer. 

7.  Each  resident  engineer  shall   be  aided  by  one  rodman,  competent  to 
use  transit  and  level,  two  tapemen,  and  one  axeman,  until  the  line  is  cross 
sectioned.    Thereafter  one  tapeman  may  be  dispensed  with.      Special  as- 
signments of  force  will  be  made,  when  necessary,  to  divisions   which  in- 
clude large  tunnels.    Each  resident  engineer  shall  have  power  to  appoint, 
suspend  or  remove  his  own  subordinates,  subject  to  the  approval  of  the 
division  engineer. 

8.  Good  discipline  and  orderly  management   require  that  all  official 
communications,  verbal  or  written,  shall  pass  from  the  superior  to  his  im- 
mediate subordinate,  or  from  the  subordinate  to  his  immediate  superior. 
Should  any  emergency  necessitate  a  deviation  from  this  rule,  the  party 
intermediately  concerned  should  be  informed  of  it. 


II.   PREPARATORY    WORK. 

1.  First  of   all,  division  engineers  shall  cause  the  centre  line  of  location 
on  their  respective  divisions  to  be  accurately  retraced,  established  and 
test -leveled. 

2.  This  done,  they  shall   furnish  promptly  to  the  associate  engineer  a 
map  in  duplicate  of  their  respective  divisions,  scale  four  hundred  feet  to 
an  inch,  one  copy  to  be  on  mounted  drawing  paper,  the  other  on  tracing 
linen,  showing  the  centre  line  and  proposed  right-of-way  boundaries  in  red; 
intersected  and  adjacent  property  lines  with  names  of  owners,  political 
boundaries,  contours,  streams,  roads,  woodland,  buildings,  and  other  ob- 
jects proper  to  a  working  map,  in  black;  also  a  profile,  similarly  duplica- 
ted, to  "Plate  A"  scale,  upon  which  shall  be  marked  the  estimated  quan- 
tities in  each  cut  and  fill,  the  character  of  the  material,  the  alignment 
corresponding  to  map,  and  the  proposed  grade  line,  the  latter  to  be  pen- 
ciled on  the  paper  duplicate  and  drawn  very  finely  on  the  tracing  in  red, 
with  its  rates  per  centum  and  elevations  of  change  points  clearly  figured. 

3.  The  paper  copy  of  each  of  said  duplicates  will  be  returned,  with 


PREPARATORY  WORK. 


67 


such  alterations  as  the  chief  engineer  may  think  proper  to  make  or 
approve,  and  endorsed  with  his  approval,  or  that  of  his  associate,  to  the 
division  engineer,  who  shall  place  them  on  file  in  his  office. 

4.  Thereafter  no  change  of  line  or  grade  will  be  permitted,  excepting 
upon  compliance  with  the  like  form  of  procedure,  namely:   The  submis- 
sion of  duplicate  drawings  of  the  change  proposed,  and  the  return  of 
copies  approved  by  the  chief  engineer  or  his  associate. 

5.  Division  engineers  shall  cause  to  be  prepared  for  each  of  their 
Residents  copies,  from  the  foregoing  approved  map  and  profile,  of  the 
respective  subdivisions,  and  also  a  pencil  record  of  location,  in  the  fol- 
lowing form,  to  be  called  the  "Location  Record,  Div.  No.    .    .    Subdiv.' 
No. 


Sta. 

Deflec. 

Align- 
ment. 

Mag. 
Course. 

Gradient. 

ELEVATION. 

Cross 
Sections. 

Remarks. 

Ground. 

Grade. 

6.  In  the  station  column,  transit  points  should  be  marked  with  a  circle, 
as  usual,  and  turning  points  inclosed  with  a  triangle  in  addition  to  the 
circle.     Directly  below  every  turning  point  record  the  note  should  be 
made,  "B.  S.  to  .  •  .     .     ."  indicating  the  backsight  point;  and  in  the 
deflection  column  should  be  recorded  the  total  deflection,  at  each  turning 
point,  from  the  range  of  backsight  to  that  of  foresight.    By  means  of 
such  a  record  the  line  can  in  future  be  retraced,  not  only  over  the  same 
points,  but,  failing  one  or  more  of  them,  with  the  same  angles  used  on 
the  establishment  of  location. 

7.  The  alignment  column  must  show  the  calculated  course  and  the 
length  of  each  tangent,  thus;  N.  64°  35'.  W.— 3,972  feet;  and  the  degree, 
length,  angle,  and  apex  distance  of  each  curve,  thus:  5°  C.   R.  (or  L.) — 
650  ft.;  angle,  32°  30';  A.  D.  334  feet. 

8.  The  column  of  remarks  should  contain,  notes  of  benches,    land, 
stream,  timber,  and  road  lines,  and  other  matters  of  interest  relating  to 
the  line   or  the  work  to  be  constructed.     The    cross-section    columns 
should  be  reserved.     Stations  should  be  entered  on  every  third  line  of  the 
book  only,  thereby  recording  about  eight  hundred  feet  per  page,  to  pro- 
vide for  subsequent  additions. 

9.  The  original  book  from  which  the  copies  are  made,  should  be  re- 
tained by  the  division  engineer. 


68  RIGHT  OF  WAY. 

HI.   RIGHT  OF  WAY. 

1.  Division  engineers  shall    next   cause  the   necessary   surveys   for 
right-of-way  to  be  made,  and  maps  thereof  to  be  prepared  on  "Topo- 
graphy" paper,  scale  two  hundred  feet  to  an  inch,  showing  the  plan  of 
land  to  be  taken,  the  contents  of  severalties  in  acres  and  hundredths,  the 
Township,   County  and  State  wherein  situated,  owners'  names,  road 
crossings,  streams,  buildings,  woodland,  meridian  line,  and  other  objects 
needful  or  useful  in  such  an  exhibit. 

2.  These  maps  shall  be   consecutively  numbered,  and  shall  have  a 
blank  margin  two  inches  wide  on  the  left  edge,  that  they  may  be  bound 
in  volumes  for  the  Company's  archives.    When  more  than  one  property 
is  represented  on  a  sheet,  the  severalties  shall  be  designated  by  the  sheet 
number  and  an  annex  letter,  "a,"  "6,"  etc. 

3.  Division  engineers  shall  furnish  to  the  land    agent  appointed   by 
the  Company,  when  requested  by  him,  a  tracing  from  these  maps  num- 
bered and  sub-lettered  to  correspond  with  the  original,  together  with  a 
description  of  each  property,  for  incorporation  with  the  deeds. 

4.  Currently    with      the     purchase     of    right-of-way,    or    as    soon 
thereafter    as    more    important    service    shall   permit,    division    en- 
gineers shall  cause    the    boundaries    of   the    Company's    property  to 
be  marked  by  corner  and  line  stones,  or  other  endurable  monuments. 
This  should  be  done  before  ground  is  broken,  if  possible,  and  said  monu- 
ments should  be  carefully  maintained  during  the  progress  of  construction. 

5.  Division  engineers,  in  laying  out  proposed  land  purchases  on  the 
maps,  prescribed  in  (II. ,  2,)  should  provide  amply  for  station  grounds 
extra  tracks,  borrow  pits,  and  spoil  banks,  and  call  attention  thereto  by 
explanatory  notes  on  said  maps. 

6.  The  lay-out  shall  be  for  a  double-track  railroad,  tracks  thirteen 
feet  between  centres.    Sixty  feet  shall  be  the  minimum  width  taken 
in  any  case,  without  the  express  approval  of  the  chief   engineer  or 
his  associate ;  and  as  a  general  rule,  a  berm  twelve  feet  wide  on  each 
side  of  the  road  formation  shall  be  included  in  the  Company's  right- 
of-way. 

7.  The  Company's  boundary  line  shall  generally  be  parallel  to  the 
centre  line  of  the  railroad,  and  right-of-way  widths  shall  change  by  jogs 
square  to  said  centre  line,  excepting  at  the  bounds  of  severalties,  where 
changes  of  width  should  be  located,  whenever  convenient,  and  conform- 
ably to  existing  land  lines. 


FINAL  PREPARATIONS  FOR  CONSTRUCTION.  69 

IV.  FINAL  PREPARATIONS  FOR  CONSTRUCTION. 

1.  The  centre  line  having  been  established  and  test-leveled,  agreeably 
to  (II.,!,)  it  should  now  be  gone  over  with  the  level  very  carefully, 
setting  stakes  at  "grade"  points  and  at  changes  of  surface  necessitating 
additional  cross-sections,  marking  the  variations  on  the  backs  of  centre 
stakes,  noting  the  elevations  of  roads,  stream  beds  and  high  water  lines, 
and  making  new  bench  marks  at  intervals  of  about  one  thousand  feet, 
preferably  near  the  sites  of  structures  and  heavy  cuts,  where  most 
needed,  and  out  of  the  way  of  probable  disturbance. 

2.  Then  traverse  the  line  again  with  the  transit,  over  the  old  points 
and  with  the  same  deflections  recorded  on  the  establishment  of  the  loca- 
tion if  found  correct,  trueing  the  interpolated  stakes  last  set  by  level, 
and  placing  and  referencing  centre  plugs  at  "grade"    points,   grade 
summits,  and  wherever  else  they  are  likely  to  be  convenient  during 
construction. 

3.  Any  discrepancies  in  line  or  level  with  former  work,  discovered 
during  these  operations,  should  be  reported  immediately  to  the  division 
engineer. 

4.  Slope  staking  follows  next    in  order.      Division    engineers    shall 
personally  ascertain  the  probable  character  of  the  material  in  excavations, 
boring  or  sinking  test  pits  when,  in  their  judgment,  the  importance  of 
such  knowledge  warrants  it ;  and  they  will  instruct  their  subordinates 
as  to  the  formation  slopes  to  be  adopted  in  every  questionable  case. 

5.  In  addition  to  setting  the  usual  grade  and  slope  stakes,  the  ground 
should  be  cross-sectioned  a  sufficient  width  to  provide  for  possible  slips, 
further  changes  of  slope,  or  a  four-track  road.    Stakes  or  plugs  should  be 
firmly  driven  at  these  limit  points  of  observation,  whether  the  work  be  in 
cut  or  fill,  in  range  crosswise  with  the  centre  and  slope  stakes,  which 
should  always  be  placed  at  right  angles  to  the  road  axis,  their  distance 
from  centre  line  and  elevations  as  to  grade  being  noted  for  record,  and 
for  use  if  needed  subsequently.     They  may  prove  to  be  very  convenient 
during  construction  at    cuts  through   uncertain    material,    and    when 
measuring  for  estimates. 

6.  On   hillsides    where  the  road  bed   is  partly    in     excavation  and 
partly    in     embankment,    its     dimensions     shall    be    compounded    of 
those  given  in  the  standard    drawings    for  excavation  and   embank- 
ment. 

7.  Borrow  pits,  grading  at  stations,  ditches^anii^aU  other  incidental 


70  STRUCTURE  PLANS. 

excavations,  should  be  staked  and  recorded  with  the  same  exactness 
as  the  road  formation.  They  should  be  worked  in  a  regular  manner,  so 
as  to  be  readily  measured,  and  present  a  shapely  appearance  after  com- 
pletion. 

8.  Masses  of  rock  found  in  cuts  and  isolated  from  the  slopes  should  be 
measured  and  recorded  in  the  proper  books  and  shown  in  the  cross-section 
drawings. 

9.  The  accurate  establishment  and  subsequent  protection  of  tunnel 
lines  should  claim  the  early  personal  attention  of  division  engineers. 
They  will  be  duly  authorized   by  the  chief  engineer  to  acquire  the 
temporary  use  of  ground  for  observatories  and  guide  lines  outside  the 
Company's  right-of-way,  when  expedient  to  do  so. 

10.  The  alignment  and  levels  at  tunnel  sites  should  be  retraced  and  re- 
peated until  the  possibility  of  error  is  reduced  to  an  unimportant  mini- 
mum.   Such  work  is  best  done  early  in  the  day,  while  the  air  is  equable 
and  free  from  refractory  currents. 

11.  Resident  engineers  shall  personally  attend  to  the  staking  of  all  found- 
ation pits.     Before  masonry  is  started,  the  division  engineer  should  inspect 
such  pits,  and  assure  himself  by  sounding  or  otherwise,  that  they  are  of 
sufficient  depth  and  firmness.    When  judged  prudent,  the  bottom  earth 
should  be  compacted  with  rammers. 

12.  Currently  with  the  foregoing  operations,  the  location  record,  pre- 
scribed in  (II.,  5,)  should  be  perfected  by  the  addition  of  the  cross-section 
notes,  and  the  latter  line  and  level  notes,  and  all  permanently  entered  in 
ink. 

13.  Division  engineers  should  traverse  their  charges  weekly.    Resident 
engineers  should  be  constantly  on  the  line  by  day,  excepting  when  foul 
weather  or  important  office  work  prevents.    They  should  give  grade  and 
line  weekly,  and  whenever  asked  by  contractors.     They  are  thus  in  the 
way  of  correcting  errors  at  the  outset,  of  instructing  foremen  seasonably 
to  prevent  errors,  and  of  ascertaining  the  various  character  of  material 
for  estimates,  to  the  furtherance  of  the  work  and  the  due  service  of  the 
contractors,  who  should  not  have  reasonable  ground  for  dissatisfaction 
with  this  department. 

V.  STRUCTURE  PLANS. 

1.  The  chief  engineer  will  cause  standard  drawings  of  the  road  forma- 
tion and  ordinary  structures  to  be  furnished  to  each  division  office.    Di- 


FIELD  AND  OFFICE  RECORDS.  71 

vision  engineers  shall  supply  duplicates  of  these  drawings  to  their  resident 
engineers,  as  needed. 

2.  Division  engineers  shall  cause  necessary  modifications  to  be  made 
in  masonry  plans  to  adapt  them  to  various  localities,  altering  the  flare  or 
length  of  wing  wall,  for  example,  to  fit  irregular  ground,  skewing  for 
oblique  channels  or  roads,  sizing  for  heights  intermediate  to  those  pro- 
vided for  in  the  standards,  and  the  like  ;  but  the  elevations  and  square 
widths  of  bridge  seats  shall  not  be  altered  except  by  warrant  from  the 
chief  engineer  or  his  associate. 

3.  Special  instructions  will  be  given   as    to   structures  on   steep  in- 
clines and  skew  openings  sharper  than  forty-five  degrees  from  the  centre 
line. 

4.  Plans  modified  by  division  engineers,  and  also  the  standard  struc- 
tures which  they  propose  as  being  anywhere  suitable,  shall  have  the 
approval  of  the  chief  engineer  or  his  associate  before  the  work  is  laid 
out. 

5.  Where   special   structures   are   required,  such  as  viaducts,  large 
bridges,  or  other  exceptional  work,  not  provided  for  in  the  standard 
plans,  the  division  engineer  shall  cause  the  ground  to  be  surveyed  and 
mapped  to  five  feet  contours  j  scale,  ten  feet  to  an  inch,  with  correspond- 
ing profile,  and  submit  the  same,  accompanied  by  illustrative  notes  and 
such  suggestions    as   he  may  think   proper  to  add,  to  the  associate 
engineer,  who  will,  thereupon,  cause  a  plan  to  be  made,  or  give  orders 
for  its  making  to  the  division  engineer.    Exhibits  of  this  kind  should 
include  high  and  low  water  marks,  character  of  bottom  or  sub-soil,  and, 
in  the  cases  of  road-crossings,  a  profile  of  the  same  for  five  hundred  feet 
each  way. 

6.  All  plans  of  railroad  buildings  shall  originate  at  the  central  office, 
and  copies  thereof  will  be  furnished  by  the  chief  engineer  or  his  associate, 
with  suitable  instructions,  to  the  division  or  principal  assistant  engineer 
charged  with  their  erection. 

7.  Copies  of  all  plans  prepared  by  division  engineers  for  their  residents 
shall  be  preserved  in  the  division  office. 


VI.  FIELD  AND  OFFICE  RECORDS. 

1.  Resident  engineers  shall  prepare  a  series  of  cross-section  drawings, 
including  the  tunnels,  of  their  respective  subdivisions,  in  bound  books  of 
uniform  size  furnished  for  that  purpose,  showing  the  original  surface  of 


72  FIELD  AND  OFFICE  RECORDS. 

the  ground  as  widely  as  observations  extend,  the  slope  staking  for  road 
formation,  the  staking  for  incidental  excavations,  the  proposed  formation 
lines,  and  the  computed  quantities  before  grading,  in  India  ink;  copies,  or 
written  abstracts,  of  which  cross-sections  they  shall  transmit  to  the  divis- 
ion engineer  from  time  to  time  as  they  are  made,  marked  with  the  name 
of  the  division  and  other  distinguishing  particulars. 

2.  On  completion  of  each  road-section  the  resident   engineer   shall 
amend  and  perfect  his  original  cross-section  book  by  drawing  thereon,  in 
permanent  red,  the  actual  formation  as  completed,  showing  the  parting 
lines  between  various  classes  of  material,  and  the  actual  quantities  of  said 
various  classes  as  contained  in  the  final  estimate  of  the  graduation  of  said 
road-section;  together  with  a  statement  of  the  cost  of  said  graduation  to 
the  contractors  and  the  Company,  which  amendments  the  division  engi- 
neer shall  thereupon  cause  to  be  incorporated  in  his  own  copies  of  the 
cross-sections,  after  revision  by  him,  and  shall,  when  requested,  or  on  the 
completion  of  the  work,  transmit  the  originals  to  the  associate  engineer, 
endorsed  with  his  approval. 

3.  The  statement  of  cost  to  the  contractor  should  comprise,  as  nearly 
as  can  be  ascertained,  the  value  per  item,  and  the  amount  of  labor, 
material,  use  of  tools  and  machinery,  superintendence  and  sundries, 
distributed  and  assigned  in  such  detail  as  information  on  hand  shall  war- 
rant.   The  statement  of  cost  to  the  Company  should  be  a  summary  of  the 
final  estimate. 

4.  The  cross-section  books  will  be  paged  with  consecutive  numbers;  no 
erasures  shall  be  made  in  them,  nor  shall  any  leaf  be  removed  therefrom 
for  any  cause  whatsoever.    If  errors  occur  cancel  the  page  in  such  manner 
as  not  to  obscure  the  errors,  and  use  the  next  page. 

5.  Resident  engineers  shall  also  prepare  a  series  of  masonry  drawings, 
on  white  paper  sheets  of  uniform  size  furnished  for  the  purpose,  in  which 
all  such  structures,  including  drain  pipes,  shall  be  represented  on  a  scale 
of  four  feet  to  the  inch,  or  eight  feet  to  the  inch,  as  the  division  engineer 
may  prescribe  for  structures  of  various  magnitude.    Such  drawings  shall 
show  the  said  structures  in  plan,  elevation,  and  section  as  actually  built, 
inclusive  of  foundations,  foundation  pits,  substructure  if  any,  grade  line, 
and  elevations  of  leading  details.    There  shall  be  also  a  legend  on  the 
drawings  of  each  separate  structure,  stating  clearly  the  actual  quantities 
of  the  various  classes  of  work  included  in  the  final  estimate,  and  a  sum- 
mary, such  as  is  prescribed  for  graduation,  of  the  actual  cost  to  the  con- 
tractors and  to  the  Company. 


FIELD  AND  OFFICE  RECORDS-  73 

6.  On  the  completion  of  each  subdivision  said  cross-section,  tunnel  and 
masonry  drawings  shall  be  transmitted  to  the  division  engineer,  and  by 
him,  when  so  requested,  after  correction  therefrom  of  the  copies  on  his 
files,  transmitted,  with  his  approval  affixed,  to  the  associate  engineer. 

7.  Each  drawing  of  the  two  sets  described  above  shall  be  exactly  local- 
ized, in  its  title,  with  the  name  of  the  division,  subdivison,  section,  sta- 
tion and  plus. 

8.  Each  division  engineer,  at  or  before  the  time  of  transmitting  his 
first  monthly  estimate,  shall  send  to  the  associate  engineer  a  complete 
profile,  on  mounted  "Plate  A,"  paper,  of  his  division,  showing  align- 
ments, gradients,  and  other  full  details  as  finally  established  for  construc- 
tion. 

9.  Then,  and  thereafter  with  each  monthly  estimate,  he  shall  forward 
to  the  associate  engineer  tracing  exhibits,  or  written  memoranda,  indi- 
cating the  condition  of  the  work  at  the  date  of  said  estimate,  from  his 
progress  profile,  in  order  that  the  progress  profile  in  the  central  office 
may  be  supplemented  to  match. 

10.  All  progress  profiles  shall  represent  the  work  done    during  each 
month  in  transparent  washes  of  color,  as  follows: 

January Carmine.  July, Scarlet. 

February Green.  August Dark  Green. 

March Yellow.  September Orange. 

April Cobali  Blue.  October Purple. 

May, Burnt  Sienna.  November Burnt   Umber. 

June Black.  December Gray. 

11.  Division  engineer  shall  cause  to  be  prepared,  on  mounted  white 
roll  paper,  a  complete  map  and  profile  of  his  division,  horizontal  scale 
four  hundred  feet,  vertical  scale  forty  feet  to  an  inch,  both  on  the  same 
sheet,  showing  the  centre  line,  grade  line,  and  land  lines  of  the  road  in 
red,  streams  in  blue,  brick  and  frame  buildings  in  carmine  and  burnt 
sienna  respectively,  faintly  colored;  all  other  details  in  India  ink,  with  ten 
feet  contours  finely  drawn,  each  even  hundred  slightly  heavied,  and  the 
outer  limits  of  road  formation — that  is  to  say,  the  crests  of  cuts  and  the 
toes  of  fills— indicated  in  plan  by  dotted  lines.    This  document  to  lie  on 
the  stocks  in  the  division  office,  gradually  perfecting,   and  finally  in- 
cluding all  the  company's  lands  and  buildings,  together  with  such  sup- 
plemental plans,  to  larger  scales,  as  the  chief  engineer  shall  order,  of  town 
properties  or  particular  reaches  of  the  road,  whereupon  it  shall  be  filed 


74 


FIELD  AND  OFFICE  RECORDS. 


in  the  central  office  as  a  permanent  record.  The  above  map  should  em- 
brace, if  possible,  all  the  topography  obtained  during  the  surveys 
within  one  mile  on 'each  side  of  the  located  line,  and  should  be  neatly  and 
accurately  executed. 

12.  Each  division  engineer,  contemporaneously  with  the  foregoing  map 
and  profile,  shall  cause  to  be  prepared  a  complete  record  and  description, 
by  sections,  of  the  finished  roadway  on  his  division,  after  the  following 
general  form,  to  be  furnished  from  the  central  office  : 


Div.  No.. 


Sec.  No.. 


RT.    OB 

ELKVT. 

.. 

i 

CROSS 

GRADUATION  C.  Y. 

WAY. 

*  . 

SECTIONS. 

1 

Jf 

a 

^ 

Q 

Allign't. 

0 

3' 

L. 

R. 

Ground. 

Grade. 

Gradient 

°t 
1 

L. 

c. 

R. 

1 

Loose  R. 

.a 
1 

2 

w 

Found. 

MASONRY  CLASSES  C.    YDS. 

Misc. 

DESCRIPTION  OF 

Miscell. 

Remarks. 

1. 

2. 

3. 

4. 

Mas'y  struc- 
tures. 

Bridges  and 
viaducts. 

13.  To  the  record  of  each  road  section  shall  be  appended  a  summary 
or  the  final  estimate  for  said  section,  as  paid  by  the  company,  and  the 
column  of  remarks  shall  contain  the  miscellaneous  notes  from  office  rec- 
ords previously  compiled,   together  with  such  other  information,  as  to 
boundary  monuments  or  plusses,  bench  marks,  foundations  and  sundries, 
as  may  be  of  use  on  future  enlargements  of  the  road-bed  and  right-of-way. 

14.  Division  engineers  shall  require  periodically  from  their  subordi- 
nates the  data  necessary  for  the  compilation  of  this  record.    On  its  com- 
pletion they  will  entitle  it,  adding  a  brief  description  of  the  division,  its 
locality  and  terminal  points,  and  transmit  the  record  to  the  associate 
engineer,  endorsed  with  their  approval,  for  the  company's  archives. 

15.  Resident  engineers  ehall  keep  a  series  of  field  books,  to  be  called 
"  Construction  Notes,"  one  of  which  shall  be  always  borne  about  them, 
and  used  for  recording  their  daily  doings,  noted  on  the  spot,  with  day, 
date,  and  locality  specified.     In  these  books  all  field  operations  relating 
to  the  work  of  the  contractors  shall  be  calculated  and  entered,  such  as  the 
giving  of  line  or  grade,  setting  or  re-setting  cross-section  stakes,  laying 


FIELD  AND  OFFICE  RECORDS.  75 

\ 

out  tunnels  and  structures,  measurements  for  estimate,  dimensions  and 
depths  of  foundation  pits,  coffer-dams,  elevation  of  bridge  seats,  verbal 
orders  given  to  the  contractors  or  their  agents  ;  in  short,  all  their  trans- 
actions and  observations  on  the  line,  together  with  a  diary  of  office  work. 
The  current  volume  of  this  series  should  be  delivered  to  the  rodman  for 
his  use,  if  charged  with  separate  field  duties,  in  case  of  the  absence  or 
disability  of  the  resident.  These  books  will  be  numbered  consecutively 
and  plainly  marked,  on  the  outside,  with  the  names  of  the  division  and 
subdivision,  and  the  periods  of  time  covered  by  them.  They  shall  be  pre- 
served with  great  care,  and  turned  in  to  the  division  engineer  on  the 
completion  of  the  respective  subdivisions,  or  when  called  for. 

16.  Resident  engineers  shall  use  and  preserve  bound  books,  to  be  fur- 
nished from  the  central  office,  instead  of  the  common  scratch-blocks,  for 
office    calculations,    drafts   of    estimates,  all    figuring  of    exhibits  or 
return  called  for  by  the  division  engineer,  and  statements  by  others  enti- 
tled to  them,  with  day  and  date  noted  at  the  time  of  each  entry.     These 
books  shall  be  called  "  Blotters,"  and  shall  be  numbered  and  marked  as 
prescribed  for  "  Construction  Notes." 

17.  Division  engineers  shall  keep  similar  books  for  the  record  of  their 
daily  doings  in  the  office  or  field,  and  these,  together  with  those  of  the 
resident  engineers,  shall  be  delivered  by  them  to  the  associate  engineer, 
on  the  completion  of  the  work,  or  when  called  for.     "Construction 
Notes  "  and  "  Blotters  "  shall  be  left  in  the  original  manuscript,  and  not 
inked  over  in  pencil.     If  errors  occur,  cancel  in  such  manner  as  to  leave 
them  legible,   and  insert  the  corrected  work  further  on,  noting  the  former 
as  erroneous,  and  referring  to  the  latter. 

18.  Division,  principal  assistant  and  resident  engineers  shall  preserve 
press  copies  of  all  official  written  communications  sent  out  by  them,  in 
bound  volumes,  to  be  properly  titled  and  indexed,  and  handed  into  the 
central  office  on  completion  of  the  work.  They  shall  indorse  and  preserve 
all  like  communications  received  to  the  same  end. 

19.  Principal  assistant  and  division  engineers  will  be  supplied  with 
copies  of  the  contracts  and  specifications  relating  to  their  charges.     They 
may  be  commissioned  by  authority  of  the  chief  engineer  to  negotiate 
contracts  for  labor,  material  or  right  of  way  in  special  cases,  but  all  such 
contracts  must  be  conditioned  on  the  approval  of  the  chief  engineer,  f 
signed  by  himself  or  other  immediate  representatives  of  the  company,  and 
the  orignals  filed  in  the  central  office. 


76  INSPECTORS  AND  TIME  KEEPERS. 

20.  All  subordinates  of  this  department  responsible  for  the  right  con- 
duct of  work,  shall  hold  the  contractors  to  its  timely  and  proper  execu- 
tion, in  accordance  with  the  terms  of  the  agreement  and  the  requirements 
of   the    specification.      They  should  not  only    be  vigilant  to  prevent 
any  hindrance  to  the  contractors,  but  active  and  prompt  to  keep  well  in 
advance  of  them,  so  that  there  shall  be  no  just  cause  of  complaint  for 
lack  of  stakes  or  instructions.     All  official  communications  to  the  con- 
tractors should  be  clear  and  explicit,  and  respectful  in  tone,  and  should 
be  recorded  at  the  time,  as  herein  elsewhere  directed.    Orders  and  in- 
structions shall  be  given  in  writing,  when  asked  for  by  any  contractor, 
sub-contractor  or  foreman. 

21.  Should  it  appear,  in  any  case,  that  the  conditions  of  a  contract  are 
likely  to  fail  of  fulfillment  as  to  time  of  completion  or  otherwise,  the  as- 
sociate engineer  shall  be  seasonably  informed  of  it,  with  a  statement  of 
the  causes.    Any  radical  remedies  provided  for  in  the  contract  must  be 
administered  by  the  chief  engineer  only,  or  by  express  authority  from 
him. 

22.  All  maps,  drawings,  papers  and  books  should  be  clearly  marked 
with  titles,  numbers  and  characters,  and  orderly  bestowed  and  cata- 
logued for  ready  reference  in  the  offices  of  this  department.    Division  en- 
gineers should  see  that  their  subordinates  conform  to  this  rule,  and  they 
should  at  frequent  intervals  inspect  the  instruments  furnished  their  sub- 
divisions, to  make  sure  that  they  are  kept  in  adjustment  and  not  ill- 
used. 

23.  No  original  records  shall  be  permitted  to  leave  the  respective  offices, 
excepting  as  herein  prescribed.     Other  departments  or  agencies  of  the 
company  entitled  to  information  from  this  department  must  be  served 
by  copy  only,  and  not  by  the  original  drawings,  sections  or  records,  unless 
the  chief  engineer  expressly  warrants  a  deviation  from  the  rule. 

24.  All  regulations  herein  contained  for  the  government  of  line  engi- 
neers proper  shall  govern  principal  assistants  and  others  in  the  special 
service  of  the  department,  to  whom  they  are  cleary  applicable. 


VH.   INSPECTORS  AND  TIME  KEEPERS. 

1.  Division  engineers  will  be  authorized,  when  it  appears  proper  to  the 
chief  engineer,  to  employ  inspectors  for  important  structures.  Such  in- 
spectors shall  receive  orders  from  and  report  directly  to  the  resident  en- 


ESTIMATES.  77 

gineer.     Division  engineers  will  instruct  their  residents  as  to  the  duties 
of  inspectors. 

2.  Each  division  engineer  may,  by  like  authority,   employ  a  general 
time  keeper,  whose  duty  it  shall  be  to  keep  a  correct  record  of  the  labor 
and  machinery  employed  on  the  work,   properly  classified  and  located, 
the  wages  paid,  materials  expended,  and  other  notes  concerning  the  prog- 
ress of  the  work  and  the  contractor's  outlay. 

3.  The  time  keeper  shall  act  under  the  immediate  orders  of  the  divi- 
sion engineer.     Resident  engineers  and  their  subordinates  should  be  in- 
structed to  co-operate  with  him,  and  he  shall  have  power  to  employ 
additional  help,  subject  to  the  approval  of  the  division  engineer,  in  the 
event  of  their  assistance  proving  inadequate. 

4.  He  should  report  weekly  to  the  division  engineer,  and  hand  in  a 
monthly  statement  of  the  force  account  of  each  subdivision,  properly 
distributed,  for  reference  by  the  division  engineer  of  the  residents. 

5.  Resident    engineers    and    their    subordinates    should    be    so    con- 
stantly on  the  line  as  to  obtain  an  independent  force  account,   approxi- 
mately correct,  for  themselves.     This  they  shall  do,  for  comparison  with 
that  furnished  by  the  division  engineer,  should  a  general  time  keeper 
be  employed  ;  and,  in  case  of  any  unaccountable  discrepancy,  call  his 
attention  to  it. 

6.  Division  engineers  shall  make  monthly  returns  of  force  accounts, 
with  their  monthly  estimates  to  the  Associate  engineer,  after  a  form  pro- 
vided by  the  central  office. 

7.  Division  engineers  shall  keep  a  book  of  force  accounts,  showing  the 
items  properly  classified  and  distributed,  and  will  compare  and  harmonize 
notes  with  the  Residents  when  making  up  the  Road  Section  Records 
herein  prescribed  (VI.  12). 


VIII.    ESTIMATES. 

1.  On  or  about  the  27th  of  each  month,  resident  engineers  shall  take 
measurements  and  make  an  estimate  of  the  work  done  on  each  section  of 
their  respective  subdivisions  during  the  month  current,  statements  of 
which  estimates  they  shall  prepare  in  duplicate  on  prescribed  forms, 
one  copy  to  be  retained,  the  other  to  be  delivered  to  the  division  engi- 
neer not  later  than  the  first  day  of  the  month  following  that  to  whicl^ 
they  refer, 


78  ACCOUNTS,  SUPPLIES  AND  SUNDRIES. 

2.  Division  engineers  shall  prepare  like  estimates  of  the  work  done  on 
each  section  of   their    respective  divisions  in  quadruplicate  and  send 
three  copies,  duly  authenticated,  to  the  associate  engineer,  not  later 
than  the  fifth  day  of  the  month  following   that  to   which  they  refer, 
accompanied  by  a  force  account,  a  recapitulation  of  work  after  such 
forms  as  may  be  provided,  and  abstracts  for  the  progress  profile  herein 
before  described  (VI. ,  9).     One  copy  of  the  estimate  sheets  and  accom- 
panying    papers,    excepting   progress   data,  will   be   retained   on   his 
office  file. 

3.  Quantities  greater  than  those  due  to  the  net  measure,  as  defined  by 
the  slope  staking,  the  masonry  plans  or  prescribed  tunnel  sections  shall 
not  be  allowed  in  either  the  monthly  or  the  final  estimates  ;   provided, 
however,  that  any  extra  expense  incurred  shall   be  clearly  the  result 
of  slovenly  conductor  violation  of  orders.    If  unsuitably  slope-staked,  if 
drawings  are  erroneous,  or  if  slips  occur  in  cuts  and  falls  in  tunnels  from 
causes  not  reasonably  to  have  been  forecast  and  prevented,  the  extra  work 
done    may  be  covered  by  estimate,  under  instructions  from  the  chief 
engineer. 

4.  In  classifying  estimates,  the  quality  of  masonry  and  the  character  of 
material  removed,  as  described  in  the  specifications,  shall  be  regarded  ex- 
clusively of  all  other  considerations.    If  any  case  of  losing  merit  occurs, 
employes  in  this  department  must  bear  in  mind  that  such  case  is  for  the 
judgment  and  the  action  solely  of  those  who  pay  the  money,  the  engi- 
neer's duty  being  rigorous  adherence  to  the  requirements  of  the  contract 
and  specifications. 

5.  No  employes  of  this  department  shall  be  interested  in  any  contract, 
or  in  the  furnishing  of  contractors'  supplies  on  the  line  of  the  road,  or  in 
any  business  connected  therewith,  excepting  that  of  the  Company. 


IX.    ACCOUNTS,  SUPPLIES  AND  SUNDRIES. 

1.  The  pay-rolls  and  expense  accounts  for  each  month  shall  be  pre- 
pared by  the  division  engineers  and  transmitted,  with  their  endorse- 
ments, on  or  before  the  fifth  day  of  the  month  following,  to  the  associate 
engineer. 

2.  After  approval  in  the  central  office,  checks  will  be  sent  to  the  division 
engineers  for  each  individual  to  whom  payment  appears  to  be  due,  and 
the  receipted  pay  rolls  and  expense  vouchers  shall  then  be  returned  to  the, 
associate  engineer, 


MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS.  79 

\ 

3.  Division  engineers  shall  book  the  salary  and  expense  accounts  of 
their  respective  divisions  in  the  usual  form,  and  shall  report  all  discharges, 
appointments  and  transfers  to  the  associate  engineer  at  the  time  of  such 
transactions. 

4.  The  fixed  salaries  of  the  employes  of  this  department  shall  be  in  full 
for  all  service  and  personal  expense,  excepting  necessary  outlays  on  the 
Company's  business,  for  transportation  and  subsistence,  by  division  engi- 
neers or  their  draughtsmen  when  called  away  from  the  Division  Head- 
quarters, and  by  resident  engineers  or  their  subordinates  when  called 
away  from  their  Subdivisions. 

5.  Division    engineers   shall   make    formal    requisition    on    the    as- 
sociate engineer  for  necessary  equipment  and  supplies.     They  shall  keep 
a  record  of  all  company  property  in  their  charge,  and  make  report  there- 
of quarterly,  with  inventory  of  articles  on  hand  at  date  of  previous  report, 
received  since,  expended,  in  what  manner  or  service,  and  on  hand  at 
date  of  current  report,  adding  explanatory  remarks. 

6.  Under  the  head  of  incidental  expenses  shall  be  included,  and  item- 
ized, minor  outlays  for  stationary  and  printing,  office  rent,  fuel,  lights 
and  attendance,  tools  and  repairs  thereof,  postage,  telegraph  and  express 
charges,  messengers  on  special  errands  requiring  certainty  and  dispatch, 
and  such  small  stores,  needed  in  the  progress  of  the  work,  as  can  best  be 
obtained  on  the  ground.     la  these  matters,  and  in  the  conduct  of  their 
charges  generally,  division  engineers  are  expected  to  practice  a  watch- 
ful and  rational  economy  and  to  exact  it  of  their  sub  rdinates,  Incorrect 
estimates,  slovenly  records,  laziness,  drunkenness,  erroneous  field  work, 
bungling  use  of  instruments  to  their  injury,  squandering  of  road  supplies 
for  private  account  and  the  like  should  be  followed  by  quick  riddance  of 
the  culprit. 

7.  Offices  should  not  be  lounging  places,  and  great  care  must  be  taken 
that  no  unauthorized  persons  have  access  to  books,  papers,  or  other  infor- 
mation relating  to  the  work. 

8.  No  person  appointed  to  or  discharged  from  the  company's  service  in 
this  Department,  shall  be  allowed  expenses  to  or  from  the  field  of  service. 


X.  MISCELLANEOUS   INSTRUCTIONS  AND  SUGGESTIONS. 

1.  In  slope  staking,  when  material  is  doubtful,  stake  for  rock.  In  such 
cases  where  earth  cuts  are  started  vertical,  have  a  force  to  follow  closely 
with  trimmed  slopes,  to  avoid  irregular  breaks  and  slips.  Set  side  stakes 


80  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

every  fifty  feet  for  trimmers.  After  stripping  rock  restake  for  it.  Leave 
a  berm  of  four  feet  bet  ween  foot  of  earth  slope  and  crest  of  rock  in  mixed 
cuts. 

2.  All  curves  should  be  slope-staked  at  intervals  of  fifty  feet. 

8.  Where  cut  is  in  excess,  have  it  wasted  regularly  along  the  convexed 
side  of  curve  in  adjacent  fill,  unless  the  possibility  of  flattening  the  curve 
in  future  makes  it  expedient  to  waste  on  the  concave  side.  Waste  sym- 
metrically on  tangents  ;  if  single  track,  on  double  track  side, — subject 
to  the  condition  that  no  overhaul  shall  be  required  and  no  increase  of 
masonry,  except  by  warrant  from  the  central  office. 

4.  Where  fill  is  in  excess  on  single  track,  first  double  track  the  adjacent 
cuts  for  a  supply,  if  earth,  and  within  overhaul  limit.      Should  more  ma- 
terial be  needed,  widen  earth  cuts  to  their  utmost,  leaving  in  every  case 
room  for  berm  ditch  and  additional  four  feet  for  fence  berm. 

5.  Waste  no  material  above  grade  unless  imperative  and  authorized  by 
the  division  engineer.      Where  material  is  permitted  thus  to  be  wasted, 
leave  in  every  case  a  berm  of  not  less  than  ten  feet,  and  additional  allow- 
ance for  future  extra  track. 

6.  Be  vigilant  to  prevent  tresspass  on  adjacent  properties  in  making 
side  ditches,  spoil  banks,  or  otherwise. 

7.  Side  and  berm  ditches  should  be  opened  in  advance  of  graduation 
and  kept  open.  Material  from  berm  ditches  should  be  ridged  up  regularly 
on  down  hill  side;  that  from  side  ditches  deposited  in  embankment.      See 
that  the  outfall  from  ditches  in  cuts  is  turned  aside  so  as  not  to  scour  the 
fills. 

8.  Where  stream  channels  are  changed  the  new  channel  should  be  side 
sloped,  and  a  berm  of  twelve  feet,  with  allowance  for  future  extra  track, 
left  between  its  crest  and  foot  of  embankment. 

9.  On  bare  slopes,  to  be  embanked,  plow  the  ground  lengthwise  before 
filling  in,  and  on  very  steep  hillsides  excavate  terrace  benches  to  hold  the 
embankment. 

10.  Examine  embankment  sites  for  springs  and  have  them  carefully 
drained  clear  of  the  formation,  by  ditches  filled  with  broken  stone  or 
cobbles. 

11.  Finish  all  earth  or  mixed  embankments,  full  width  at  top  and  four 
per  centum  of  the  record  center  height  above  grade  for  the  reception  of 
ballast;  rock  embankments,  two  per  centum.    This  is  tentative,  and  sub- 
ject to  modification.    It  is  believed  to  be  sufficient  allowance  for  embank- 


MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS.  81 

merits  made  in  layers  or  with  scraper,  and  approximately  correct  for 
heavy  dumped  work  on  good  bottom,  which,  advancing  more  slowly,  must 
needs  have  gotten  to  its  bearing  in  some  measure  before  completion. 
Division  engineers  are  invited  to  give  their  past  experience  on  this  point, 
and  also  to  profit  by  their  present  opportunity  for  more  knowledge  con- 
cerning it. 

12.  In  rock  cuts  see  that  no  large  masses,  dislodged  by  blasting,  are  al- 
lowed to  remain  on  the  slopes  or  overhanging  them,      Examine  all  such 
masses  with  bars,  and,  where  liable  to  be  washed  or  frosted  down,  have 
them  removed  and  duly  entered  in  the  estimates. 

13.  Require  rock  cuts  and  tunnels  to  be  taken  out  full  width  and  depth 
at  once,  and  suffer  no  bottoming  to  be  left  over  except  by  special  permis- 
sion of  the  chief  engineer,  in  tunnels  only,  for  the  purpose  of  drainage 
during  construction. 

14.  See  that  the  road  is  graded  true  to  line,  and  as  staked  out ;   that 
material  needed  elsewhere  is  not  wasted  at  mouths  of   cuts  ;    that  side 
slopes  in  excavations  are  plane  surfaces,  not  convex  ;  that  embankments 
are  carried  out  the  full  width  due  to  the  slope  staking  at  whatever  level 
built ;   that  their  slopes  are  plane  surfaces,  not  concave  ;    that  they  are 
built  in  layers  back  of  all  abutment  and  culvert  walls  ;    that  the  centres 
of  arch  culverts  are  allowed  generally  to  remain  until  the  embankment 
has  been  carried  by  them  ;    and,  if  removed,  that  the  embankment  is 
built  in  layers  a  proper  height  above  crown  of  arch. 

15.  Approaches  to  crossings,  in  excavation  or  embankment,  should  be 
graded  not  less  than  twelve  feet  wide  on  top,  and  up  to  the  height  of  top 
of  rail— say  two  feet  above  the  grade  of  formation  ;  they  should  ramp  or 
slope  at  a  rate  not  exceeding  one  in  ten,  and  be  level  a  sufficient  distance 
each  side  of  the  railroad  to  prevent  the  possibility  of  stone  or  timber 
trucks  stalling  on  the  track. 

16.  Meeting  grades  should  be  rounded  off  with  vertical  curves  at  least 
six  hundred  feet  long;  and  as  much  longer,  especially  in  the  case  of  pock- 
ets, or  cylindrical  grades,  as  economical  conditions  will  permit.      Special 
instructions  will  be  given  on  this  subject. 

17.  Be  cautious  not  to  allow  full  measure  in  monthly  estimates  before 
the  work  is  settled,  surfaced  and  trimmed;  a  safe  reserve  should  be  held 
usually  for  such  items. 

18.  In  retracing  line  during  construction,  or  after  graduation,  use  the 
original  turning  points  established  on  the  final  revision  of  the  line. 


82  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

19.  Timber  and  brash  should  be  cleared  the  full  width  of  right-of- 
way,  and  valuable  timber  piled  up  along  the  right-of-way,  and  saved 
for  the  company,  where  the  clearing  is  done  by  the  contractor.     Trees  on 
abutting  properties  whose  accidental  fall  might  encumber  the  track, 
should  be  legally  condemned  and  felled. 

20.  Avoid  small  openings  in  the  roadbed,  using  box  or  arch  culverts 
preferably. 

21.  The  road-bed  should  be  trimmed  to  a  crown  of  three  inches  above 
grade  in  the  middle,  to  promote  lateral  drainage  under  the  ballast. 

22.  Sound  doubtful  foundation  pits  with  an  iron  rod,  and  make  sure 
of  a  good  bottom.    Drain  them  when  feasible.    Where  not  liable  to  wash 
or  to  subsequent  exposure,  two  feet  of  gravel,  shingle  or  broken  stone, 
well  rammed,  makes  an  excellent  foundation  course. 

23.  See  particularly  to  the  deep  and  safe  founding  of  walls  and  curbs 
at  the  outfall  end  of  drainage  structures. 

24.  Before  sizing  opens  for  culverts  and  bridges  search  the  water  down 
stream  for  some  point  where  flood  volume  is  well  marked,  and  work  by 
that. 

25.  Observe  and  report  streams  suitable  for  water  supply. 

26.  Insist  on  specification  requirements  in  masonry.      Make  it  clearly 
understood  that  no  excess  of  neat  work  beyond  scale  plans  will  be  esti- 
mated.    No  crushable  chips.    No  grouting  unless  specially  authorized. 
Flush  up  solid  instead,  with  mortar  as  stiff  as  it  will  work  readily.    Good 
bond  imperative,  and  to  take  precedence  of  outside  looks. 

27.  Clear   away   the    surplus   stone   and   wreckage   from    masonry 
sites  after  the  jobs    are  done ;    and  before   the   completion   of    each 
section,  have  blasted  rock  and  all  other  cumber  accumulated  during 
construction  removed  from  adjacent  properties  and  highways. 

28.  In  establishing  outside  tunnel  lines  by  daylight,  the  best  time  has 
been  found  to  be  just  after  sunrise,  and  the  best  sight  pole  a  half -inch 
round  iron  rod  painted  white.      Plummet  lamps,  on  clear  calm  nights, 
have  given  better  results  than  sight  poles  by  day,  being  distinctly  visible 
at  long  distances. 

29.  To  transfer  line  down  a  shaft,  set  transit  point  at  a  distance  there- 
from of  about  twenty-five  feet,  from  which  point,  with  a  long  foresight, 
two  staples  or  other  guides,  may  be  ranged  on  the  side  timbers  overhang- 
ing the  pit,  and  the  centre  line  thence  plumbed  to  the  bottom  with  fine 


•MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS.  83 

.  copper  wires,  bobbed  as  heavily  as  they  can  bear,  the  bobs  immersed  in 
water.  It  has  been  necessary  in  some  cases  to  box  in  the  wires,  to  pro- 
tect them  against  water  and  air  currents.  Careful  manipulation,  patient 
and  repeated  observations,  and  a  discreet  average  of  them  are  required 
for  a  correct  transfer. 

30.  The  range  at  bottom  must  be  transferred  to  wooden  roof  plugs,  in 
which  eyescrews,  staples  or  other  suitable  fixtures  are  ranged,  and  from 
which  plummet  lamps  may  be  hung  when  required. 

31.  Bench  marks  are  established  similarly  in  the  roof,  being  stubs  of 
steel  fastened  into  holes  or  chinks,  the  elevations  of  which  are  obtained 
by  means  of  a  reversed  rod.      The  levels  may  be  transferred  from  the 
surface  with  a  steel  tape  or  wooden  rods. 

32.  All  centre  points  and  bench  marks  should  be  placed  out  of  danger 
from  rocks  thrown  by  blasting. 

33.  Standard  measures  should  be  made  at  the  outset  by  which  to  test, 
from  time  to  time,  the  tapes,  level  rods  and  other  field  measures  used  on 
the  work,  as  it  is  important  that  these  measures  be  uniform,  and  guarded 
against  change. 

34.  For  leveling  underground  a  target  with  a  diamond-shaped  opening 
in  it  has  been  found  convenient,  one  of  the  diagonals  of  said  opening  being 
horizontal.    The  rod  is  plumbed  with  a  portable  level  bubble  made  for 
the  purpose,  and  a  light  is  held  behind  the  target  at  the  time  of  observa- 
tion. 

35.  Division  engineers  will  supplement  these  general  memoranda  as  to 
tunnel  surveying,  and  will  find  room  for  their  ingenuity  in  expanding 
and  diversifying  them  to  suit  various  practice. 

'36.  Eequire  tie-contractors  to  pile  the  ties  regularly,  both  ends  visible, 
and  spaced  suitably  for  inspection,  within  not  less  than  fifteen  feet  nor 
more  than  forty  feet  from  the  centre  line  of  double-track  road  bed,  and 
not  over  two  feet  below  grade,  when  the  nature  of  the  ground  will 
admit  of  compliance  with  this  rule.  When  it  will  not,  then  require  them 
to  be  delivered  and  piled  where  they  can  be  conveniently  got  at  by  the 
tracklayers. 

37.  After  tracklaying,  and  before  opening  the  road  to  traffic,  a  flat  car 
should  be  run  its  whole  length  each  way,  with  templates,  fixable  cross- 
wise, for  testing  the  clear  width  of  rock  cuts  and  dimensions  of  tunnel 
sections.  Every  point  encroaching  on  the  standard  section  should  be 


84  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

marked  with  red  paint  from  a  large  "  whitewash"  brush,  and  removed 
promptly  by  a  floating  gang. 

38.  The  terms  " grade  line "  and  "grade,"  as  herein  used,  refer  to  the 
surface  of  the  road  bed,  at  the  established  profile  grade  ;  that  is  to  say, 
to  the  bottoms  of  cuts  and  the  tops  of  fills,  as  prepared  for  the  reception 
of  any  crowning  to  promote  lateral  drainage  and  of  the  railway  proper, 
or  superstructure,  comprising  ballast,  ties  and  rails.     The  term  subgrade 
is  omitted  as  superfluous  and  confusing,  and  is  not  to  be  used  on  this 
road.    The  elevations  of  bridge  seats,  bridge  structures  and  their  parts, 
foundations,  piers,  trestle-work,  rails,  cross-ties,  and  all  other  details 
requiriDg  such  reference  shall  be  referred  to  the  elevation  of  "  grade,"  by 
plus  and  minus  signs. 

39.  Some  of  the  rules  contained  in  this  article  are  intended  to  be  sug- 
gestive   rather     than    mandatory — practical    hints    and     instructions. 
Division  engineers  and  all  others  concerned  are  invited  to  report  any 
discrepancies,  errors  or  deficiencies,  which  they  may  observe,  either  here 
or  elsewhere,  in  the  present  compilation,  and  to  suggest  what  they  judge 
to  be  improvements,  corrections  or  useful  additions.      Regard  any  rules 
as  invalid  which  may  appear  to  conflict  with  provisions  in  the  contract 
and  specifications,  or  to  call  for  expense  not  therein  contemplated. 

WM.   F.    SHUNK; 

APPROVED  :  Associate  Engineer. 

ROBT.   H.   SAYRE, 

Chief  Engineer. 


HOWE  TRUSS  BRIDGES. 

In  ENGINEERING  NEWS  of  April  26,  1890,  a  double  page  lithographed 
inset  was  published,  showing  27  strain  sheets  and  sizes  of  members  for 
Howe  truss  bridges  from  30  feet  to  150  feet  span,  sent  by  Chief  Engineer 
A.  A.  Schenck,  of  the  Oregon  Pacific  Railway  Co.,  and  which  we  believe 
to  be  safe  and  careful  designs,  in  accordance  with  the  latest  and  best 
practice  in  wooden  bridge  construction,  which  for  a  long  time  to  come 
will  be  an  important  department  of  American  engineering  work,  although 
one  of  continually  decreasing  relative  importance. 

One  fact  we  should  especially  call  attention  to,  that  these  bridges  are 
designed  for  a  region  where  very  long  timber  is  readily  obtained,  and  is 
no  more  expensive  than  short  timbers,  so  that  the  sections  given  for  lower 
chord  would  be  much  weaker  in  proportion  to  regions  where  equally  long 
timber  was  not  available.  The  great  difference  in  the  amount  of  iron 
required  when  the  rods  are  upset  or  not  upset,  is  curiously  shown  in  the 
table  of  data  herewith  reprinted; 


TABLE  OF  DATA. 

1 
W.  Iron.  Lbs. 
Bods  upset. 

No.  of  Span. 

Assumed  loading 
per  foot. 

Total  load  per 
foot.  Ibs. 

Estimate  of  Quantities. 

h 

H 

It 

500 
« 

14 

EH^ 

8S* 

S« 
JM 

EH£ 

a 
Ij 

\F 

JU 

cT 

1... 
2                   

360 
360 
400 
400 
450 
450 
540 
540 
600 
600 
620 
620 
720 
720 
720 
800 
800 
880 
880 
940 
940 
1,000 
1,000 
1,050 
1,050 
1,100 
1,100 

5,060 
5,060 
4,600 
4,600 
4,200 
4,200 
3,860 
3,860 
3,640 
3,640 
3,600 
3,600 
3,560 
3,560 
3,560 
3,500 
3,500 
3,400 
3,400 
3,300 
3,300 
3,200 
3,200 
3,150 
3,150 
3,100 
3,100 

5,620 
5,920 
5.500 
5,500 
5,150 
5,150 
4,900 
4,900 
4,740 
4,740 
4,720 
4,720 
4,780 
4,780 
4,780 
4,800 
4,800 
4,780 
4,780 
4,740 
4,740 
4,700 
4,700 
4,700 
4,700 
4,700 
4,700 

10,165 
6,750 
13,358 
9,362 
19.025 
12,861 
22,785 
20.702 
29,931 
27,617 
35,388 
32,764 
42,709 
41,883 
40,690 
48,892 
46,454 
54,767 
50,295 
62,038 
59,254 
70,128 
66,779 
78,156 
76,323 
86.632 
86,053 

2,170 
1,930 
2.960 
3,280 
5,610 
4,710 
6,790 
5,900 
9,260 
8,420 
11,660 
10,190 
15,170 
17,880 
13,220 
22,580 
18.040 
25,820 
19,400 
30,890 
23,080 
37,050 
27,930 
40,820 
32,640 
48,090 
39,630 

,970 
1,210 
1,070 
1,550 
2,880 
2,830 
3,660 
3,830 
8,260 
7,980 
9,790 
9,730 
12,530 
12,260 
12,710 
14,290 
13,990 
15,930 
14,050 
18,290 
16,520 
20,830 
20,460 
23,210 
23,260 
27,060 
27,140 

8,210 
7,610 
10,260 
9,120 
13,440 
15,150 
11,820 
18,950 
16,040 
22,290 
16,320 
26,010 
19,580 
30,180 
23,560 
33,020 
27,360 
39,140 
33,390 

3  
4.               

5  

6           

7           

8 

9  

10 

11 

12  
13 

14          

15                   ... 

16 

17 

18 

19 

20                    .... 

21             

22 

23  :  

24                      

25.. 

26  ... 

27 

86 


HOWE  TRUSS  BRIDGES. 


Strains  given  are  for  one  truss,  and  in  1,000  pounds^ 

Sections  given  are  for  one  truss  (rods  assumed  not  upset). 

Loads  in  above  table  are  for  two  trusses. 

Strains  are  those  due  to  dead  load  -f  maximum  from  moving  load. 

A  ssumed  live  loads  are  intended  to  fully  equal  (in  strains  produced)  those  given 
in  diagram  below. 

Load  on  a  floor  beam,  14,000  pounds,  on  a  panel  length  of  chord  as  a  beam ;  36,COO 
pounds  on  an  axle. 

Wrought  iron  in  tension,  10,000  pounds  (net  section  at  root  of  thread)  per 
square  inch . 

Wood  (in  compression  only)  1-6  to  1-8  of  breaking  load  by  Smith's  formula. 

Wood  (in  tension  only)  usually  SOOpounds  to  1,000 pounds,  (500  pounds  to  800  pounds 
in  shortest  span),  per  square  inch ;  and  as  packed  beam  maximum  section  (net  sec- 
tion) 800  tc  1,000  pounds, 

LATERAL  SYSTEMS. 

DECK  SPANS— A  uniform  load  of  150  pounds  per  foot  (each  system),  J^  of  it  at  feet 
of  rods. 

A  moving  load  of  150  pounds  per  foot  (each  system),  all  of  it  at  feet  of  rods. 

Sway  braces  at  each  panel  assumed  to  equalize  the  strains  so  that  each  system  is 
the  same  (except  end  rods). 

THROUGH  SPANS— A  uniform  load  of  150  pounds  to  200  pounds  per  foot  (each  sys- 
tem). A  moving  load  of  300  pounds  per  foot  (lower  system). 

Iron  13,000  to  15,000  pounds  per  square  inch  net.    Timber  1-4  to  1-5  breaking  load. 

The  spans  included  in  the  diagrams  are  : 


30  ft.  half -through  and  deck. 

40  " 
50  " 
60  " 
70  "  ;  .  "  " 


100  ft.  through,  and  deck. 

110  " 

120  " 

13G  " 

140  " 

150  " 


90  "  through,  half -through  and  deck. 

This  includes  in  all  27  different  trusses,  covering  the  entire  "range 
usually  required  for  wooden  trusses,  spans  exceeding  150  feet  being  rare- 
ly built  of  wood. 

In  a  letter  transmitting  these  strain  sheets,  Mr.  "W.  A.  DOANE,  M.  Am. 
Soc.  C.  E.,  gives  the  following  further  details: 


Fig.  1.    Top  Chord  End  Joints  for  Howe  Truss  Spans  up  to  90  ft. 


HOWE  TRUSS  BRIDGES. 


87 


"  Howe  truss  bridges,  not  yet  having  had  their  day — at  least  in  the 
South  and  West— I  send  you  a  set  of  strain  sheets  from  30  feet  to  150  feet 
spans,  designed  for  heavy  traffic.  They  require  little  explanation  be- 
yond that  given  by  the  attached  notes  and  table  of  data. 

It  is  intended  to  use  upset  rods  for  all  spans  above  60  or  70  feet,  although 
diameters  given  are  those  required  to  give  the  necessary  area  at  root  of 
thread.  The  table  of  data  gives  approximate  weights  in  each  case.  As 
will  be  seen,  from  1,000  to  9,000  pounds  of  iron  per  span  are  saved  by  up- 
setting the  ends  of  rods. 

It  is  believed  that  some  details  of  construction  have  been  improved  in 
these  designs. 

"  Fig.  1  (enlarged  scale)  shows  the  general  style  of  joints  at  junction  of 
top  chord  with  end  mains  for  all  through  spans  up  to  90  feet. 


Fig.  3.    Portal  Bracing  for  Howe  Truss  Through  Spans  of  90  ft, 

and  over. 


88  HOWE  TRUSS  BRIDGES. 

"  Fig.  3  shows  general  style  of  portal  bracing,  etc.,  for  through  spans 
over  90  feet,  these  having  a  system  of  top  lateral  bracing.  In  no  case  are 
vertical  end  posts  used  to  meet  a  useless  prolongation  of  top  chord  in 
through  spans. 

"  For  spans  of  100  feet  and  over,  the  usual  style  of  cast  brace  blocks  is 
followed,  having  tubes  slightly  let  in  to  chord  timbers  and  long  enough 
to  reach  the  opposite  face  of  chord  and  receive  the  strain  transmitted 
from  the  rods  through  the  plates.  These  latter  are  in  all  cases  made  un- 
usually wide,  however. 

"  In  spans  less  than  100  feet  the  tubes  are  dispensed  with,  and  a  block 
of  the  style  shown  in  Fig.  2  is  used,  having  a  full  bearing  on  the  chord 
as  well  as  for  the  braces,  while  the  radial  longitudinal  ribs  greatly  in- 
crease the  strength.  The  open  ends  are  not  objectionable." 


Fig.  2.    Cast  Brace-Block  for  Howe  Truss  Spans  under  100  ft. 

It  was  not  practicable  to  reproduce  the  sheet  of  diagrams  for  this  book. 
The  reader  who  wishes  to  post  himself  on  the  best  practice  in  Howe  truss 
construction  can  consult  the  number  of  the  journal  in  which  the  diagrams 
are  published. 


Table  for  Computing  Right  of  Way  Areas— TOtto  100  Ft. 


$* 

ing 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

•° 

.9 

0... 

1... 

2.. 
3... 
4... 
,5... 
6... 
7... 
8... 
9... 
10... 
11 

0.000 
0.230 
0.460 
0.690 
0.920 
1.150 
1.380 
1.C10 
1.840 
2.070 
2.300 
2  530 

0.023 
0.253 
0.483 
0.713 
0.943 
1.173 
1  403 
1.633 
1.863 
2.093 
2.323 
2  553 

0.046 
0.276 
0.506 
0.736 
0  966 
1.196 
1.426 
1.656 
1.886 
2.116 
2.346 
2  576 

0.069 
0.299 
0.529 
0.759 
0.989 
1.219 
1.449 
1.679 
1.909 
2.139 
2.369 
2  599 

0.092 
0.322 
0.552 
0.782 
012 
.242 
.472 
.702 
.932 
2.162 
2.392 
2  622 

0.115 
0.345 
0.575 
0.805 
.035 
265 
.495 
.725 
.955 
2.185 
2.415 
2  645 

0.138 
0.368 
0.598 
0.828 
.058 
.288 
.518 
.748 
.978 
2.208 
2.438 
2  66S 

0.161 
0.391 
0.621 
0.851 
1.081 
1.311 
1.541 
1.771 
2.001 
2.231 
2.461 
2  691 

0.184 
0.414 
0.644 
0.874 
1.104 
1.334 
1.564 
1.794 
2.034 
2.254 
2.484 
2  714 

0.207 
0.437 
0.667 
0.897 
1.127 
1.357 
1.587 
1.817 
2.047 
2.277 
2.507 
2  737 

.01 
.02 
.03 
.04 
.05 
.06 
.07 
.08 
.09 
.10 

Feet. 
.0023 
.0046 
.0069 
.0092 
.0115 
.0138 
.0161 
.0184 
.0207 
.0230 

12... 
13... 
14... 

2.760 
2.990 
3  220 

2.783 
3.013 
3  243 

2.806 
3.036 
3.266 

2.829 
3.059 
3  289 

2.852 
3.082 
3  312 

2.875 
3.105 
3.335 

2.898 
3  128 
3  358 

2.921 
3.151 
3  381 

2.944 
3.174 
3.404 

2.967 
3.197 
3  427 



15... 
16. 

3.450 
3  680 

3.473 
3  703 

3.496 
3.726 

3  519 
3.749 

3.542 

3  772 

3.565 
3  795 

3.588 
3  818 

3.611 
3  841 

3.634 
3  864 

3.657 

3.887 

.... 



17 

3  910 

3  933 

3  956 

3  979 

4  002 

4  025 

4  048 

071 

4  094 

4  117 

18 

4  140 

4  163 

4  186 

4  209 

4  232 

4  255 

4  278 

301 

4  334 

4  347 

19 

4  370 

4  393 

4  416 

4  439 

4  462 

4  485 

4  508 

531 

4  554 

4  577 

20 

4  600 

4  623 

4  646 

4  669 

4  692 

4  715 

4  738 

761 

4  784 

4  807 

21... 
22... 
23... 

4  830 
5.060 
5  290 

4.853 
5.083 
5  313 

4.876 
5.106 
5  336 

4.899 
5.129 
5  359 

4.922 
5.152 
5  382 

4.945 
5.175 
5  405 

4.968 
5.198 
5  428 

.991 
5.221 
5  451 

5.014 
5.244 
5  474 

5.037 
5.267 
5  497 

.... 



24  .. 

5  520 

5  543 

5  566 

5  589 

5  612 

5  635 

5  658 

5  681 

5  704 

5  727 

25... 

5  750 

5.773 

5  796 

5  819 

5  842 

5  865 

5  888 

5  911 

5  934 

5  957 

26... 

27 

5.980 
6  210 

6.003 
6  233 

6.026 
6  256 

6.049 
6  279 

6.072 
6  302 

6.095 
6  325 

6.118 
6  348 

6.141 
6  371 

6.164 
6  394 

6.187 
6  417 



28... 
29... 

6.440 
6.670 

6.463 
6.693 

6.486 
6.716 

6.509 
6  739 

6.532 
6  762 

6.555 
6  785 

6.578 
6  808 

6.601 
6  831 

6.624 
6  854 

6.647 

6.877 

.... 



30... 

6.900 

6.923 

6.946 

6.969 

6.992 

7.015 

7.038 

7.061 

7.084 

7.107 

.... 



Having  the  distance  between  the  boundaries  of  the  tract  through  which  the  line 
passes,  find  the  number  of  stations  in  the  left  hand  column  and  in  the  column  of 
tenths  under  .0  to  0.9  will  be  found  the  acres  required,  if  the  plus  is  an  even  10  ft.  If 
the  plus  contains  odd  feet  the  correction  to  be  added  is  found  in  the  column  of  feet. 

Engineering  News.  E.  A.  D.  PARKER, 

Kearney,  Neb, 


PILE  DRIVING  MACHINE. 

The  machine  illustrated  is  one  of  the  very  latest  in  model,  and  the 
heaviest  in  New  York  harbor. 


Tjg.3. 

—  Plan  of  Guides  8f  .Bect-piecea 


JTianA. 

Cross  j>ec.-lonff. bulkheada  


Details  of  Pile  Driving  Machine. 


PILE  DRIVING  MACHINE.  01 

The  hull  is  56  ft.  6  ins.  long  and  23  ft.  6  ins.  wide  over  all;  each  of  the 
sides  of  the  hull  is  made  of  four  pieces  of  yellow  pine,  the  two  lower  each 
8  X  14  in.,  the  third  7  X  14  in.,  the  top  piece  6  X  14  in.,  all  securely  tied 
by  through  bolts;  the  bow  planking  is -oak,  5  ins.  thick;  the  bottom  and 
end  plank  yellow  pine,  3  ins.  thick.  The  bow  is  further  strengthened  by 
a  16  X  16  in.  cross  timber  at  top,  and  at  the  stern  is  an  8  X  12-in.  cross 
timber  of  yellow  pine.  Oak  is  used  on  the  bow  as  being  better  adapted 
to  stand  the  constant  wear  of  the  piles  hauled  against  it,  and  to  prevent 
knots  or  inequalities  on  the  piles  interfering  with  their  position  under  the 
hammer;  the  bow  planking  overhangs  6  ins.  in  its  total  height. 

The  chief  end  in  the  design  of  a  hull  for  a  floating  pile  driver  is  to 
obtain  longitudinal  stiffness,  so  that  the  strains  between  the  bow  and 
engine  may  be  properly  distributed.  To  this  end  our  hull  is  strengthened 
lengthwise  by  four  wooden  bulkheads  or  kelsons,  each  6  ins.  thick  (Fig.  2) 
and  braced  laterally  by  four  sets  of  X  braces  of  6  X  6  'timber.  The  hull 
is  further  braced  in  the  center  by  two  3  X  12  in.  Y.  P.  braces,  and  tie  rods 
or  "hog  chains"  of  iron,  If  ins.  in  diameter.  Wale  pieces  and  fender 
plank  3  ins.  thick  protect  the  outside  of  the  hull  against  chafing;  the  deck 
has  a  "crown"  of  about  6  ins.  in  its  total  width. 

The  hammer-guides  are  made  of  two  pieces  of  12x12  Y.  P.  67  feet 
long  from  out  to  out  with  inside  guides  of  5x4  in.  stuff  protected  by 
plate  iron  J  ins.  thick ;  f-in.  bolts  with  countersunk  heads  fasten  the 
inner  guides  to  the  main  sticks  and  at  the  same  time  secure  the  iron  work 
to  the  same.  The  bottoms  of  the  main  guides  are  connected  with  the 
12x12  bed  pieces,  shown  in  Fig.  3,  by  two  timber  knees,  and  are  tied  at 
top  by  the  cap  shown  in  Fig.  6. 

The  dimensions  and  general  arrangement  of  the  back-bracing  is  fully 
shown  in  Figs.  1  and  3  ;  the  bolts  used  in  this  portion  of  the  frame  work 
are  $  in.  diameter.  The  side  braces  are  round  timbers  16-ins.  diameter 
at  the  butt,  and  they  are  anchored  to  the  hull  by  two  heavy  timber 
knees  to  each.  The  bed  pieces,  as  shown  at  Fig.  3,  are  fastened  down  to 
the  hull  by  four  bolts  each,  1  in.  in  diameter,  the  forward  bolts  passing 
through  the  16xl6-in.  oak  piece  on  bow,  and  the  after-bolts  passing 
into  a  cross  timber  6x  14  ins. ,  as  shown  at  Fig.  4.  The  foot  of  the  back- 
bracing  is  secured  to  the  bed  timbers  by  one  1  in.  strap-bolt  in  each 
timber,  the  strap  portion  of  bolt  being  2Xi  in.  in  section.  A  £-in. 
through-bolt  ties  the  three  braces  together. 

The  iron  stay-rods  running  from  head  of  guides  to  after  part  of  hull 
are  two  in  number,  and  are  each  1  in.  in  diameter. 


56'  6- 


•Lonff.Sec.  showing  internal  bracmff.  

Pile  Driving  Machine. 


PILE  DRIVING  MACHINE.  93 

The  hoisting  sheaves  on  top  are  two  in  number,  placed  side  by  side. 
They  are  12  ins.  in  working  diameter,  1£  ins.  from  out  to  out,  and 
3£  ins.  wide ;  and  the  pin  passing  through  them  is  2£  ins.  diameter 
at  the  sheaves,  and  2  ins.  diameter  in  the  boxes.  Experience  teaches 
that  these  proportions  are  none  too  great  to  stand  the  severe 
work  frequently  put  upon  it  in  hoisting  heavy  weights  and 
tearing  out  timber.  The  fall  rope  attached  to  the  hammer  is  2  ins.  in 
diameter,  and  the  "  runner"  used  in  hoisting  up  piles  is  If  ins.  diameter. 

The  hoisting  engine  is  a  double-drummed  Mundy  engine  of  a  nominal  25 
horse  power. 

Fig.  5  shows  the  hammer  used  with  this  machine.  The  drawing  is 
sufficient  to  show  its  general  design.  The  weight  is  3,300  Ibs. 

Fig.  7  shows  the  method  of  attaching  the  two  5  X  12  in.  horizontal 
braces  to  the  round  side  braces,  as  further  shown  in  Fig.  2. 


METRIC  RAILWAY  CURVES. 

[From  Engineering  News,  Oct.  13, 1883.] 


Several  inquiries  have  appeared  from  time  to  time  in  ENGINEERING 
NEWS  for  a  metric  table  of  railway  curves.  We  to-day  present  one  pre- 
pared by  an  engineer  who,  after  practicing  the  American  method  of  lay- 
ing out  curves  in  the  United  States,  has  been  for  two  years  occupied  in 
railroad  surveying  with  the  metric  system  in  Mexico. 

The  table  is  explained  by  the  headings  of  the  columns.  Curves  are 
designated  (as  in  the  first  column)  by  the  angle  which,  according  to  the 
American  system,  has  to  be  turned  off  repeatedly  at  a  point  on  the  cir- 
cumference, and  is  subtended  by  successive  equal  chords.  This  angle  is 
called  by  Trautwine  and  Shunk  the  "  tangential "  angle  ;  by  Henck  and 
Searles  the  "deflection"  angle.  Jn  the  first  article  of  the  appendix  to  his 
revised  edition.  Prof.  Henck  suggests  the  use  of  this  angle  for  designat- 
ing curves  run  by  the  metric  system.  An  obvious  advantage  thus  gained 
is  that  the  angle  to  be  measured  in  staking  jut  a  curve  in  a  field  is  simply 
the  angle  named  in  speaking  of  the  curve.  The  equal  chords  successively 
measured  according  to  the  metric  system  should  be  20  meters  in  length, 
as  was  abundantly  enforced  by  numerous  writers  who  discussed  the  point 
in  ENGINEERING  NEWS  a  year  and  a  half  ago.  As  to  the  adaptability  of 
that  length  to  railroad  engineering,  it  may  be  noticed  that  in  the  first  er- 
ample  of  staking  out  a  curve  given  in  Shunk's  "Field  Engineer,"  the 
length  of  chord  is  taken  to  be  20.12  m.,  which  he  calls  66  feet.  The 
stakes,  set  at  successive  20-meter  intervals,  are  to  be  marked  with  the  suc- 
cessive even  numbers,  2,  4,  6,  8,  etc. ,  so  as  to  constitute  the  dekameter  the 
unit  of  stake  numbering.  Each  stake  is  thus  designated  by  its  distance 
in  dekameters  from  the  zero  point,  and  each  kilometer  stake  is  marked 
by  an  exact  hundred.  The  angle  by  which  the  curve  changes  its  direc- 
tion per  unit  of  length  as  thus  marked  is,  therefore,  one-half  of  its 
change  of  direction  between  the  extremities  of  the  20-meter  chord; 
that  is,  it  is  exactly  the  "  20-meter  chord  "  angle  used  to  stake  it  out  and. 
to  designate  it;  and  the  total  change  of  direction  made  by  any  length  of 
the  curve  is  simply  the  product  of  this  angle  multiplied  by  the  Difference 


METRIC  RAILWAY  CURVES.  95 

in  the  numbers  of  the  stakes  at  its  beginning  and  end,  just  as  in  the  pres- 
ent practice  in  the  United  States. 

For  convenience  in  staking  fractional  parts  of  the  20-meter  chain,  the 
second  column  of  the  table  is  given,  showing  the  number  of  minutes  to 
be  turned  off  with  the  transit  per  meter,  being  simply  one-twentieth  of 
the  angle  in  the  fir>t  column.  Here  a  slight  advantage  over  the  100-ft- 
chord  is  seen,  because  60  bears  a  simpler  relation  to  20  than  to  100. 

The  column  of  radii  presents  a  simplicity  superior  to  the  100-ft.  system, 
in  that  the  metric  radius  is  just  10  times  the  co-secant  of  the  angle  in  the 
first  column,  and  can  therefore  be  taken  directly  from  a  trigonometrical 
table  by  altering  the  decimal  point,  or  in  the  case  of  the  logarithm,  the 
characteristic.  The  computation  in  the  present  United  States  practice  is 
a  little  more  complicated.  The  dfference  thereby  produced  in  the  figures 
may  be  seen  by  comparing  the  columns  of  20-meter  chord  angle  and 
radius  with  the  columns  of  degree  of  curve  and  radius  in  the  field-books 
commonly  used  in  this  country.  The  metric  radii,  instead  of  being  fig- 
ured exactly  one-tenth  of  the  expression  in  feet  corresponding  to  the 
same  angle,  have  slightly  larger  decimals.  The  discrepancy  is  so  small, 
however,  that  for  the  greater  part  of  railroad  work  the  old  tables  might 
be  used  with  the  metric  system,  by  taking  the  old  degrees  for  the  20-meter 
chord  angles  and  dividing  all  the  old  radii  by  10,  that  is,  merely  changing 
the  decimal  point  one  place.  It  is  different  with  the  figures  for  deflection 
distances  and  ordinates,  which,  in  the  metric  table,  are  almost  exactly 
four-tenths  of  what  they  are  in  the  old  tables  for  the  same  angle  in  first 
column. 

The  precise  length  of  the  curve,  in  contradistinction  to  that  of  the  chords 
by  which  it  is  staked  out,  is  seldom  required.  The  last  column  in  the 
table  is  inserted  chiefly  with  a  view  to  exhibiting  the  percentage  to  be 
added  to  such  a  chord  to  get  the  length  of  arc  it  subtends.  This  percent- 
age is  clearly  seen  when  we  move  the  decimal  point  of  the  last  column 
one  place  to  the  left;  and  it  may  be  made  useful  in  connection  with  such 
tables  as  are  given  at  the  end  of  Shunk's  "  Field  Engineer"  and  of  the  re- 
vised edition  of  Henck's  "  Field  Book."  For  example,  those  tables  give, 
among  other  very  useful  data,  the  distance  from  the  intersection  point  to 
either  extremity  of  a  one-degree  curve  whose  total  length  varies  between 
0°  and  90°.  Mr.  Shunk  calls  this  the  "apex  distance  ; "  Prof.  Henck,  the 
"tangent."  For  a  curve  90°  in  length,  Mr.  Shunk's  table  gives  5730  ft. 
Prof.  Henck's,  5729.7  ft.,  the  same,  of  course,  as  the  radius.  Either  of 
these  divided  by  10  can  be  used  in  practice  for  the  metric  1°  curve,  whose 


96 


METRIC  CURVE  TABLE. 


J5 

TJ 

rt 

1  Quarter 
Middle.)    point. 

M 

o3  ^ 

B 

DEFLECTION 

+£  "5a  •& 

*: 

®| 

«w 

ORDINATE 

|.§  S  w. 

I 

ffe 

RADIUS 

a  . 



at  distance 
from  end-chord. 

2oc| 

_H  K'C  a? 

Ed 

3a 

METERS 

From 

fo^'° 

2§ 

1? 

tan- 

r rom 
chord. 

Of  10 

Of  5m. 

§ 

S 

gent. 

in* 

HJ 

O°10' 

OJ^' 

3437.75 

3.5362745 

.058 

.116 

.Olo 

.011 

10.0000 

20' 

1' 

1718.38 

3.2352463 

.116 

.233 

.029 

.022 

10.0001 

30' 

1145.93 

3.0591581 

.175 

.349 

.044 

.033 

10.0001 

40' 

2' 

859.46 

2.9342237 

.233 

.465 

.058 

.044 

10.0002 

50' 

2Ji' 

687.57 

2.8373192 

.291 

.582 

.073 

.055 

10.0004 

1°    0' 

3' 

572.99 

2.7581447 

.349 

.698 

.087 

.065 

10.0005 

10' 

491.14 

2.6912059 

.407 

.814 

.102 

.076 

10.0007 

20' 

4' 

429.76 

2.6332231 

.405 

.931 

.116 

.087 

30' 

41^' 

382.02 

2.5820810 

.524 

1.047 

.131 

.098 

loioon 

40' 

5' 

343.82 

2.5363351 

.582 

1.163 

.145 

.109 

10.0014 

50' 

312.58 

2.4949553 

.640 

1.280 

.160 

.120 

10.0017 

2°    0' 

6' 

286.54 

2.4571808 

.698 

1.396 

.175 

.131 

10.0020 

10' 

264.51 

2.4224340 

.756 

1.512 

.189 

.142 

10.0024 

20' 

7' 

245.62 

2.3902659 

.814 

1.629 

.204 

.153 

10.0028 

30' 

7V£' 

229.26 

2.3603204 

.873 

1.745 

.218 

.164 

10.0032 

40' 

8' 

214.94 

2.3323107 

.9.31 

1.861 

.233 

.175 

10.0036 

50' 

8fcS' 

202.30 

2.3060020 

.989 

1.977 

.247 

.186 

10.0041 

3»    0' 

9' 

191.07 

2.2811998 

1.047 

2.093 

.262 

.196 

10.0046 

10' 

9^' 

181.03 

2.2577414 

1.105 

2.210 

.276 

.207 

10.0051 

20' 

10' 

171.98 

2.2354889 

1.163 

2.326 

.291 

.218 

10.0056 

30' 

163.80 

2.2143247 

1.222 

2.442 

.306 

.229 

10.0062 

40' 

11'   ^ 

156.37 

2.1941477 

1.280 

2.558 

.320 

.240 

10.0068 

50' 

149.58 

2.1748701 

1.338 

2.674 

.335 

.251 

10.0075 

4°    0' 

12' 

143.36 

2.1564155 

1.396 

2790 

.349 

.262 

10.0081 

10' 

137.63 

2.1387167 

1.454 

2.916 

.364 

.273 

10.0088 

20' 

13' 

132.35 

2.1217146 

1.512 

3.022 

.378 

.284 

10.0095 

30' 

L3V^' 

127.45 

2  1053567 

1.570 

3.138 

.393 

.295 

10.0103 

40' 

L4' 

122.91 

2.0895961 

1.629 

3.254 

.407 

.306 

10.0111 

50' 

118.68 

2.0743911 

1.687 

3.370 

.422 

.317 

10.0119 

6°    0' 

15' 

114.74 

2.0597040 

1.745 

3.486 

.437 

.328 

10.0127 

20' 

16' 

107.58 

2.0317513 

1.861 

3.718 

.466 

.349 

10.0145 

40' 

17' 

101.28 

2.0055032 

1.977 

3.950 

.495 

.371 

10.0163 

6°    0' 

18' 

95.67 

1.9807654 

2.093 

4.181 

.524 

.393 

10  0183 

20' 

19' 

90.65 

1.9573751 

2.210 

4.413 

.553 

.415 

10.0204 

40' 

20' 

86.14 

1.9351943 

2.326 

4.044 

.582 

.437 

10.0226 

7°    0' 

zy, 

82.06 

1.9141055 

2.442 

4.875 

.612 

.459 

10.0249 

20' 

78.34 

1.8940076 

2558 

5.106 

.641 

.481 

10.0274 

40' 

23' 

74.96 

1.8748128 

2.674 

5.336 

.670 

.503 

10.0299 

8°    0' 

24' 

71.85 

1.8564447 

2.790 

5.567 

.699 

.525 

10.0326 

20' 

25' 

69.00 

1.8388361 

2.906 

5.797 

.729 

.547 

10.0353 

40' 

26' 

66.36 

1.8219279 

3.022 

6.027 

.758 

.569 

1U.0382 

9°    0' 

27' 

63.92 

1.8056676 

3.138 

6.257 

.787 

.591 

10  0412 

20' 

28' 

61.66 

1.7900083 

3.254 

6.487 

.816 

.613 

10.0444 

40' 

29' 

59.55 

1.7749082 

3.370 

6.717 

.846 

.635 

10.0476 

1O°    0' 

30' 

57.59 

1.7603298 

3.486 

6.946 

.875 

.657 

10.0510 

METRIC  RAILWAY  CURVES.  97 

radius  is  572.99.  (It  would  be  still  better  in  using  the  metric  system  to 
have  a  new  table  calculated  expressly  for  radius  572.958.)  To  get  with 
very  close  approximation  the  corresponding  dimensions  for  any  other 
curve  we  divide  by  the  degree  designating  the  curve.  Hence,  for  a  90° 
length  of  a  metric  10°  curve  we  should  get  a  tangent  or  apex  distance  of 
57.30  m.  In  the  case  of  so  sharp  a  curve  the  question  arises  whether  this 
is  sufficiently  accurate  for  our  purpose,  and  this  question  is  answered  by 
reference  to  the  last  column  in  the 'metric  table.  After  moving  the  deci- 
mal point  as  above  directed,  we  find  1.0051  for  the  10°  curve,  showing  that 
our  57.30  is  in  error  by  one-half  of  one  per  cent.  To  get  exactly  the  dis- 
tance required,  multiply  5730  by  1.005,  and  we  get  57.59,  just  as  given  in 
the  metric  table  for  the  radius  of  the  10°  curve.  The  same  percentage 
correction  is  applicable  to  the  other  tabulated  data  as  well  as  to  the  tan- 
gent or  apex  distance. 

In  computations  like  that  discussed  in  the  preceding  paragraph,  the  20- 
meter  chord  has  the  advantage  over  that  of  100  ft.  that  it  is  a  shorter 
length,  and  consequently  the  arc  it  subtends  in  any  circle  differs  by  a 
smaller  percentage  from  the  chord.  Hence,  the  tabulated  data  above 
mentioned  can  be  applied  without  requiring  correction  to  a  larger  range 
of  metric  curves  than  of  the  curves  used  in  the  American  foot  practice. 
For  example,  observe  that  in  the  curves  of  b6.14  and  90.65  meters  radius 
the  percentage  is  less  than  one-quarter  of  one  per  cent.  Between  the  two 
lies  the  20°  curve,  as  given  in  the  Ame  rican  tables,  with  a  radius  of  287.9 
ft.,  in  which  the  100-ft.  chord  subtends  an  arc  of  100.5  ft.,  showing  a  per- 
centage of  one-half  of  one  percent.  Accordingly,  if  we  start  5,730  ft., 
the  tabulated  tangent  or  apex  distance  above  cited  for  90°  length  of  an 
American  lc  curve,  and  take  one-twentieth  of  it  for  the  corresponding 
dimension  of  thetcircle  of  287.9  ft.,  radius,  we  have  286.5  ft.,  and  must 
add  1.4  ft.  to  get  the  correct  value  equal  to  radius.  On  the  other  hand, 
suppose  we  had  started  with  573  meters  as  the  tangent  or  apex  distance 
in  the  metric  1°  curve,  to  get  the  corresponding  dimension  of  the  circle  of 
86.14  meters  radius  observe  that  that  circle  is  designated  by  the  20  m. 
chord  angle  of  6£°;  three-twentieths  of  573  m.  is  85.95  m.,  and  to  get  the 
correct  value  equal  to  radius  we  must  add  0.19  m.,  which  is  lees  than  half 
of  1.4  ft.,  and  less  than  one  quarter  of  one  per  cent. 

Engineers  accustomed  to  thinking  of  curves  by  their  American  desig- 
nations may  find  it  convenient  in  making  mental  comparisons  to  bear  in 
mind  that  if  any  curve  has  its  20-m.  chord  angle  multiplied  by  3,  the  pro- 
duct is  nearly  the  "  degree"  used  to  designate  the  curve  in  this  country; 


98 


METRIC  RAILT 


UNIVERSITY   OF   CALIFORNIA 
LIBRARY 


for  100  ft.  is  very  little  more  than  3 
last  spoken  of,  having  a  radius  of  86 
of  6£ °,  is  almost  the  same  as  the  Aim 
number  of  20  is  given  in  the  metric  t 
laid  off  per  meter  in  staking  out,  as 
radius;  and  all  of  the  numbers  in  tl 
minutes,  might  be  regarded  as  th< 
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ENGINEERING     NEWS     AND     AMERICAN 


RAILWAY 
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,    ,      .        I,.  11  .1   i  u  in       will  take 

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